LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNIA. 


Class 


ELECTRIC   POWER 
CONDUCTORS 


BY 

WM.  A.    DEL    MAR 

*  4 

A.  C.  G.  I.,  Assoc.  Mem.  A.  I.  E.  E.,  Assoc.  I.  E.  E.,  Assistant  Engineer  of  the 

Electrical  Transmission  Department,  New  York  Central  Railroad, 

Formerly  with  the  Interborough  Rapid  Transit  Co..  etc. 


THE 

R 

OF 


NEW  YORK: 

D.    VAN    NOSTRAND    COMPANY 
23  MURRAY  AND  27  WARREN  Sxs. 

LONDON: 

CROSBY   LOCKWOOD    &    SON 
7  STATIONERS'  HALL  COURT,  LUDGATE  HILT. 

1909 


GENERAL 


Copyright,  1909 

BY 

D.  VAN'NOSTRAND  COMPANY 


JScbrrl  0rummnnl»  anil  (Company 

Stofodt 


PREFACE 

THE  purpose  of  this  book  is  to  present,  for  the 
benefit  of  the  users  of  power  conductors,  a  clear 
account  of  all  the  engineering  considerations  which 
affect  the  purchase  and  use  of  such  conductors. 

The  book  will  be  found  practical  and  up  to  date; 
being  based  upon  notes  prepared  by  the  author  for 
his  own  use,  and  there  is  nothing  in  the  book  which 
has  been  copied  from  any  published  data  without 
having  been  thoroughly  studied  and  found  reliable. 

The  arrangement  of  the  book  follows  the  rational 
order  of  the  series  of  engineering  considerations  which 
affect  the  purchase  of  conductors,  namely,  the  deter- 
mination of  material,  insulation,  and  size,  the  specifi- 
cations, test,  and  installation. 

The  text  is  made  as  brief  as  possible,  and  where 
explanation  or  theoretical  discussion  is  advisable,  the 
text  is  supplemented  by  appendices. 

The  sections  on  Alternating  Current  Feeder  Calcu- 
lations and  Stress  in  Spans,  were  written  by  Dr.  Harold 
Fender,  who  also  suggested  the  method  of  calculation 

given  in  the  sections  on  Skin  Effect  and  Kelvin's  Law. 

iii 

203792 


iv  PREFACE 

Dr.  Fender's  method  of  calculations  are  distinguished 
for  their  thorough  adaptability  to  practical  work  with 
the  minimum  amount  of  labor  and  for  their  careful 
scientific  foundation.  The  author,  therefore,  has 
pleasure  in  expressing  his  indebtedness  to  Dr.  Fender 
for  his  valuable  contributions. 

The  author  also  acknowledges  the  courtesy  of  Mr. 
W.  W.  Weaver  of  the  Electrical  World  and  of  Mr.  J. 
H.  Smith  of  the  Electrical  Age  in  permitting  the  use 
of  material  from  their  respective  journals. 

W.  A.  DEL  MAR 

NEW  YORK,  June,  1909 


\ 

TABLE   OF   CONTENTS 


WIRES   AND    CABLES 


ERRATA. 

Page  i.       2d  line  of  table,  3d  column,  change  ".995  "  to  "3.31." 
Page  4.       22d  line,  change  "4X6°"  to  4X10°." 

/D\2        /7rD\2 
Page  14.     3d  line,  change  I—  1    to  I  —  )  . 

Page  27.    4th  line  from  bottom,  change  "  9.516  "  to  "  9.5916." 

Page  49.  To  the  note  at  the  bottom  of  Table  B,  add  "  except  for 
smaller  sizes  than  No.  0,  B.  &  S.,  where  the  divergence  between 
experiments  is  greater." 

Page  125.  Cancel  entire  paragraph  following  words  "Appendix 
IV,"  from  "If"  to  "practice"  inclusive. 

Page  284.   Line  after  first  formula  "  8n  "  should  be  "  o.oo8?r." 

Page  292.  Table  I,  column  headed  "  Error  Thickness,"  read  in 
reverse  order,  i.e.,  5/64  in.  heading  the  table  and  3/i28ths  in.  ending  it. 

Page  296.  i3th  line,  between  "4000"  and  "respectively,"  add 
"millions." 

Page  298.  Top  of  last  column,  the  number  "0.315625,"  change  to 
"0.515625." 


IV 


PREFACE 


Dr.  Fender's  method  of  calculations  are  distinguished 
for  their  thorough  adaptability  to  practical  work  with 
the  minimum  amount  of  labor  and  for  their  careful 
scientific  foundation.  The  author,  therefore,  has 
pleasure  in  expressing  his  indebtedness  to  Dr.  Fender 
for  his  valuable  contributions. 

— «j™^iic/x  Acknowledges  the  courtesy  of  Mr. 


TABLE   OF   CONTENTS 


WIRES   AND    CABLES 

CHAPTER  I 
MATERIALS  AND  GAUGES 

PAGE 

1 .  Materials i 

2.  Wires 8 

3.  Mechanical  Properties  of  Cables 12 

CHAPTER  II 
ELECTRICAL  PROPERTIES 

1 .  Resistance  of  Wires  and  Cables 22 

2.  Resistance  of  Networks 33 

3.  Skin  Effect 40 

4.  Carrying  Capacity 43 

CHAPTER  III 
INSULATION  AND  INSULATED  CONDUCTORS 

1 .  Insulation 59 

2.  Insulated  Cables 76 

3.  Insulators 94 

CHAPTER  IV 
DETERMINATION  OF  SIZE  FOR  GIVEN  VOLTAGE  DROP  AND  POWER  Loss 

1.  Voltage  and  Systems  of  Distribution 104 

2.  Lamp  Wiring  Calculations 107 

3.  Continuous  Current  Railway  Feeder  Calculations in 

4.  Negative  Booster  Calculations 127 

5.  Alternating  Current  Transmission  Line  Calculations 133 

6.  Economical  Size  of  Conductors  and  Kelvin's  Law 156 

V 


vi  TABLE   OF   CONTENTS 

CHAPTER  V 
DETERMINATION  or  SIZE  FOR  GIVEN  STRESS  IN  SPANS 159 

CHAPTER  VI 
SPECIFICATIONS 179 

CHAPTER  VII 
TESTING  WIRE  AND  CABLE 200 

CHAPTER  VIII 

INSTALLATION 

1 .  Underground  Lines 220 

2.  Overhead  Lines •. 224 

3.  Splicing 227 

CHAPTER  IX 

DEPRECIATION  AND  DETERIORATION 

1 .  Depreciation 238 

2.  Deterioration  by  Electrolysis  and  Miscellaneous  Causes 240 

CHAPTER  X 
THIRD  RAIL  CIRCUITS 245 

CHAPTER  XI 
RAIL  BONDS 252 

CHAPTER  XII 
TABLES  OF  INDUCTANCE,  REACTANCE  AND  CAPACITY 

1 .  Inductance 270 

2.  Capacity 277 

APPENDICES 

I.  BASIS  OF  B.  &  S.  GAUGE 281 

II.  BASIS  OF  SKIN  EFFECT  AND  CARRYING  CAPACITY  FORMULA 284 

III.  METHOD    OF   CALCULATING    THICKNESS    OF    RUBBER    INSULA- 

TION     291 

IV.  BASIS  OF  DIRECT   AND  ALTERNATING  CURRENT  TRANSMISSION 

FORMULAE 299 

V.  BASIS  OF  FORMULA  FOR  STRESSES  IN  SPANS 308 

VI.  EXPLANATION  OF  SPECIFICATIONS 310 

VII.  BASIS  OF  TABLES  OF  INDUCTANCE 321 


-  * 


OF  THE 

UNIVERSITY 

OF 


ELECTRIC    POWER    CON 
DUCTORS 


CHAPTER  I 
MATERIALS  AND  GAUGES 

i.  MATERIALS 

COMPARISON   OF   ALUMINUM   AND   COPPER 
General  Properties. 


Aluminum. 

Copper 
(Hard  Drawn). 

Copper, 
Soft  Drawn. 

Specific  gravity  . 

2  68 

8Q-? 

8  89 

Relative  specific  gravity  

I.OO 

3?  •? 

Conductivity        (Matthiessen's 
Standard)  

61  to  63 

06  to  99 

Elastic  limit,  solid  wire  (Ibs.  per 
sq.in.).  . 

14  ooo 

^  5  ooo  to  40  ooo 

Coefficient  of  expansion  per  de- 
gree F.  . 

o  ooo  o  i  ^  8 

Modulus  of  elasticity,  solid  wire 

8  to  16X10° 

Melting  point  (about) 

i  200°  F 

2000°  F 

2000°  F 

Lbs.  per  cu.in  

O    OO7 

O    32 

Tensile  strength,  solid  wire,  Ibs. 
per  sq.in.  . 

(20,000  to 
3  ^,000 

45,000  to 
68  ooo 

25,000  to 

3.* 


ELECTRIC   POWER  CONDUCTORS 


Comparison  of  Aluminum  and  Copper  of  Equal  Length  and 
Conductance. 

5  =  specific  gravity  of  aluminum ; 
5=  specific  gravity  of  copper; 

c  =  conductivity  of  aluminum ; 
C  =  conductivity  of  copper ; 

/  =  tensile  strength  of  aluminum,  Ibs.  per  sq.in.; 
T  =  tensile  strength  of  copper,  Ibs.  per  sq.iri.; 
p  =  price  of  aluminum,  per  Ib. 
P  =  price  of  copper,  per  Ib. 

Then  to   compare  a   given  aluminum  wire  with  a 
copper  wire  of  equal  length  and  conductance, 


Relative  cost, 
Relative  cross-section, 
Relative  diameter, 
Relative  weight, 
Relative  breaking  strength, 


Aluminum  _  spC 
Copper        SPc 

Aluminum  _  C 
Copper        c 

Aluminum  _    \C 
Copper        ^  c 

Aluminum     sC 
Copper       Sc 

Aluminum     1C 


Copper        Tc 

-D  ,  ,.  Aluminum      4IC 

Relative  current  carrying  capacity,  =\| — 

Copper         ^  c 


MATERIALS   AND   GAUGES 

The  following  table  is  calculated  for  s  =  2.68, 5  = 
25,000,  and  7  =  55,000; 


Conductivity  (Matthiessen's 
Standard). 

Copper. 

Aluminum 

98 

63 

62 

61 

60 

Relative  cost  

I.  CO 
I.OO 

I.  00 
I.OO 
1.00 

I.OO 

0.467^ 
1.556 
1.247 
0.467 
0.708 

1.117 

Q-474P 
1.581 
1.258 
0.474 
0.719 

I.  121 

0.48277 
1.  606 
1.268 
0.482 
0.731 

I.I26 

0.489? 

I-633 
1.278 
0.489 
0.743 

I.I30 

Relative  cross-section  
Relative  diameter  

Relative  weight 

Relative  breaking  strength 
Relative  current  carrying 
capacity  ^ 

*  For  wires  of  the  same  diameter  aluminum  will  carry  only  80%  of  the  current 
carried  by  copper. 

Advantages  of  Aluminum  Compared  with  Copper. 

(1)  For   equal    conductance  aluminum   is  cheaper. 
In  the  United  States  the  price  is  held  about  10%  less 
than  that  of  copper. 

(2)  For  equal  conductance  aluminum  is  lighter  and 
therefore  easier  to  string. 

(3)  Sleet  does  not  adhere  so  readily  as  to  copper. 

Disadvantages  of  Aluminum  Compared  with  Copper. 

(1)  Aluminum  wire  must  be  strung  with  a  greater 
sag  than  copper  wire  of  equal  conductance  due  to  its 
lower  tensile  strength  and  greater  surface  exposed  to 
wind  and  sleet.      For   long   spans  higher  towers  are 
therefore  required. 

(2)  Low  melting-point  makes  wire  more  liable  to 
break  off  under  influence  of  an  arc  either  at  the  insu- 


4  ELECTRIC   POWER  CONDUCTORS 

lators  or  when  foreign  wires  fall  on  the  line.  Wires 
must  therefore  be  placed  further  apart,  necessitating 
the  use  of  longer  cross  arms. 

(3)  Scrap  value  very  small  on  account  of  artificial 
price  of  new  product. 

(4)  Aluminum  is  much  softer  than  copper;   greater 
care  must  therefore  be  observed  in  stringing  to  avoid 
denting  or  abrasion. 

TENSILE   STRENGTH   AND   ELASTIC    PROPERTIES   OF   COPPER 

The  properties  of  commercial  hard-drawn  copper 
seldom  resemble  those  given  in  the  old  text-books,  as 
the  commercial  article  used  for  aerial  power  wires  is 
much  softer  than  that  usually  described  as  hard- 
drawn  copper.  The  modulus  of  elasticity  instead  of 
being  i6Xio6  (in  Ib.-in.  units)  varies  from  SXio6  to 
i6Xio6;  the  tensile  strength  instead  of  being  over 
60,000  Ibs.  per  sq.in.,  varies  from  45,000  to  68,000. 
The  point  where  the  strain  ceases  to  be  proportional 
to  the  stress,  called  the  elastic  limit,  varies  from 
35,000  to  45,000  Ibs.  per  sq.in.,  38,000  being  a  value 
easy  to  obtain.  These  values  apply  to  solid  wire; 
for  stranded  cables  the  modulus  of  elasticity  varies 
from  4  XJ0  to  12  X  io6,  the  tensile  strength  from  45,000 
to  60,000  Ibs.  per  sq.in.;  the  elastic  limit  from  25,000 
to  35,000  Ibs.  per  sq.in. 

If  the  elastic  limit  is  considerably  exceeded,  the  wire 
becomes  so  attenuated  that  the  actual  stress,  i.e., 
the  force  per  sq.in.  of  actual  section  gradually  in- 


MATERIALS   AND   GAUGES  5 

creases,  and  ultimately  teaches  a  value  sufficient  to 
break  the  wire.  Therefore  a  stress  considerably  under 
the  nominal  breaking  stress  will  break  a  wire  if  con- 
tinued for  a  sufficient  length  of  time.  Working  a  wire 
having  60,000  Ibs.  per  sq.in.  ultimate  strength,  at  a 
stress  of  10,000  Ibs.  per  sq.in.,  therefore  gives  an 
actual  safety  factor  of  less  than  six  instead  of  six, 
as  is  usually  computed. 

The  hardness  of  copper  depends  upon  the  amount 
of  drawing  it  has  been  subjected  to,  and  all  degrees 
of  hardness  are  obtainable  from  soft  annealed  copper 
to  the  hard  material  used  for  telephone  wires.  Tel- 
ephone wires  can  be  made  very  hard  because  they  are 
drawn  to  such  a  small  size.  It  is  therefore  important 
to  take  into  account  the  size  of  wire  in  specifying  its 
degree  of  hardness  and  the  various  mechanical  prop- 
erties dependent  thereon.  This  is  well  illustrated  by 
the  curves  of  Fig.  i. 

Curve  A  is  what  is  usually  called  half-hard  drawn 
and  curve  D  is  a  very  hard- drawn  telephone  wire  of 
i/ 10  inch  diameter,  having  an  elastic  limit  of  50,000 
Ibs.  and  an  ultimate  strength  of  69,000  Ibs.  per  sq.in. 
with  an  elongation  of  i%. 

It  should  be  noted  that  in  hard-drawn  copper  of 
various  degrees  of  hardness,  the  elongation  at  the 
elastic  limit  is  usually  about  J%,  whatever  the  modu- 
lus of  elasticity. 

Soft-drawn  copper  cannot  be  used  alone  in  tension 
on  account  of  its  low  elastic  limit,  about  3000  to  5000 


6 


ELECTRIC   POWER  CONDUCTORS 


Ibs.  per  sq.in.  It  is  used  with  hard-drawn  copper 
wires  for  the  cores  of  concentric  cables,  where  a  knowl- 
edge of  its  stresses  under  various  elongations  is  essen- 

A          B  C 


w 


1 


I 


10 


50 


20  30  40 

Stress,  Thousands  of  Ibs.  per  Sq.  In. 

FIG.  i. — Typiral  Stress-Strain  Diagrams,  Hard  Drawn  Copper  Wire. 

tial  for  the  calculation  of  the  strength  of  the  cable. 
Fig.  2  is  a  typical  stress  strain  diagram  for  commercial 
soft-drawn  copper,  and  is  based  on  the  following 
table: 


GAUGES   AND   MATERIALS 


Ultimate  strength 


Lbs.  per  Sq.in.  of  Original 
Area  Elastic  Limit. 

3,000 

5,000 
10,000 
15,000 
20,000 
25,000 
30,000 
3S»°oo 
40,000 
41,000 
41,500 
42,000 


15 


10 


Elongation  Per  Cent  of 
Original  Length. 

.2 

-4 
I.I 

2.1 

3-5 
5-° 
6.7 
9.0 
12.5 

13.6 
15-0 

45-o 


I  5  10  15  20  25          30  35          40 

Stress.  Thousands  of  Ibs.  per  Sq.  In. 
FIG.  2. — Typical  Stress-Strain  Diagram,  Soft  Drawn  Copper. 


45 


The  ultimate  strength  of  soft-drawn  copper  is  of  no 
practical  importance  as,  when  the  elastic  limit  is  some- 
what exceeded  and  the  load  maintained,  the  wire 
stretches  until  it  breaks.  The  ultimate  strength  var- 
ies from  25,000  to  45,000  Ibs.  per  sq.in.  with  an  elon- 
gation of  from  25%  to  45%. 


8 


ELECTRIC   POWER  CONDUCTORS 


Wire  used  for  the  core  of  hard-drawn  cables  fre- 
quently has  an  ultimate  strength  of  about  45,000  Ibs. 
per  sq.in.,  with  an  elongation  of  8%  to  10%.  The 
elastic  limit  of  such  wire  is  about  20,000  Ibs.  per  sq.in. 
and  the  modulus  8  to  10  millions. 

2.  SOLID   WIRES. 

RATING  OF  WIRES 
American  or  Brown  and  Sharpe  Gauge 


A.W.G- 
B.  &S. 

Diam- 
eter. 
Inches. 

Area. 

Copper. 

Aluminum. 

Circular 

Mils. 

Square 
Mils. 

Lbs.  per 
Foot. 

Feet  per 
Lb. 

Lbs.  per 
Foot. 

Feet  per 
Lb. 

oooo 

0.460 

211,600 

166,190 

0.6405 

1.561 

0.1929 

5-185 

ooo 

0.4096 

167,800 

131,790 

0.5080 

1.969 

0.1529 

6-539 

00 

0.3648 

133,100 

104,518 

0.4028 

2.482 

0.1213 

8.246 

0 

0.3249 

105,500 

'  82,887 

0-3195 

3-130 

0.09618 

10.40 

I 

0.2893 

83,690 

65,732 

0-2533 

3-947 

0.07629 

13.11 

2 

0.2576 

66,370 

52,128 

0.2009 

4-977 

0.06050 

16.53 

3 

0.2294 

52,630 

41,339 

0.1593 

6.276 

0.04797 

20.85 

4 

0.2043 

41,740 

32,784 

0.1264 

7.914 

0.03805 

26.28 

5 

0.1819 

335ioo 

25,999 

O.IOO2 

9.980 

o.c30I7 

33-15 

6 

0.1620 

26,250 

20,618 

0.07946 

12.58 

0.02393 

41-79 

7 

0-1443 

20,820 

l6,35l 

0.06302 

15-87 

0.01898 

52.69 

8 

0.1285 

16,510 

12,967 

0.04998 

20.  01 

0.01505 

66.44 

9 

0.1144 

13,090 

10,283 

0.03963 

25-23 

0.01193 

83-82 

10 

0.1019 

10,380 

8,155 

0.03143 

31.82 

0.009462 

105-7 

ii 

0.09074 

8,234 

6,467 

0-02493 

40.12 

0-007505 

133-2 

12 

0.08081 

6,530 

5,129 

0.01977 

50-59 

0.005952 

168.0 

13 

0.07196 

5,i78 

4,067 

0.01568 

63-79 

.004720 

211.9 

14 

0.06408 

4,107 

3,225 

0.01243 

80.44 

-003743 

267.2 

15 

0.05707 

3,257 

2,558 

0.009858 

101.4 

.002968 

336.9 

16 

0.05082 

2,583 

2,029 

0.007818 

127.9 

.002354 

424.8 

17 

0.04526 

2,048 

1,609 

0.00620O 

161.3 

.001867 

535-6 

18 

0.04030 

1,624 

1,276 

0.004917 

203.4 

.001480 

675-7 

19 

0.03589 

1,288 

1,012 

0.003899 

256-5 

.001174 

851.8 

20 

0.03196 

1,022 

802 

0.003092 

323-4 

.000931 

1074.1 

GAUGES   AND   MATERIALS 


COMBINATION    OF   WIRES   APPROXIMATELY   EQUIVALENT 
TO  ONE  WIRE 

(Based  upon  approximate  equivalence  of  \/2  and'Vga.) 


B.  &  S. 
No. 

2  Of 

B.  &  S. 
No. 

4  Of 

B.  &  S. 
No. 

8  of 
B.  &  S. 
No. 

16  of 
B.  &  S. 

No. 

32  of 
B  &  S. 
No. 

64  of 
B.  &  S. 
No. 

One  Each 
of  B.  &  S. 
Nos. 

oooo 

0 

3 

6 

9 

12 

15 

000 

i 

4 

7 

10 

13 

16 

00 

2 

5 

8 

ii 

14 

17 

i  arid  3 

0 

3 

6 

9 

12 

i-5 

18 

2  "  4 

I 

4 

7 

10 

13 

16 

3  "  5 

2 

5 

8 

ii 

14 

17 



4-6 

3 

6 

9 

12 

15 

18 

.... 

5  "  7 

4 

7 

10 

13 

16 

6-8 

5 

8 

ii 

14 

17 





7  "  9 

6 

9 

12 

15 

18 

.... 

.... 

8  "  10 

7 

IO 

T  1 

16 

0   "  II 

g 

1  7 

IO   l  *  12 

9 

12 

15 

18 

ii  -  13 

T  'J 

16 

12   "l4 

ii 

14 

17 

13   "  15 

I  2 

I  r 

18 

14  "  16 

16 

I  ^   "  17 

J3 

I  7 

16  "  18 

15 

18 

Circular  Mils.  A  circular  mil  is  the  area  of  a  circle 
of  i  mil  (thousandth  of  an  inch)  diameter.  The  area 
of  any  conductor  in  circular  mils  is  equal  to  the  square 
of  its  diameter  in  mils,  or  one  million  times  the  square 
of  its  diameter  in  inches. 

one  square  mil      4 


one  circular  mil 


10 


ELECTRIC   POWER  CONDUCTORS 


BIRMINGHAM  OR  STUBB'S  WIRE  GAUGE 


B.  W  G. 

Stubb's. 

Diameter. 
Inches. 

Area. 

Lbs.  per  Foot. 
Copper. 

Circular  Mils. 

Sq.Mils. 

oooo 

0-454 

206,100 

161,883 

0.6239 

ooo 

0.425 

180,600 

141,863 

0.5468 

00 

0.380 

144,400 

II3,4H 

0.4371 

0 

0.340 

115,600 

90,792 

0-3499 

i 

0.3000 

90,000 

70,686 

0.2724 

2 

0.2840 

80,660 

63,347 

0.2441 

3 

0.2590 

67,080 

52,685 

o.  2031 

4 

0.2380 

56,640 

44,488 

0.1715 

5 

0.2200 

48,400 

38,013 

0.1465 

6 

O.2O30 

41,210 

32,365 

0.1247 

7 

O.I80O 

32,400 

25,447 

0.09808 

8 

0.1650 

27,230 

21,382 

0.08241 

9 

0.1480 

21,900 

17,203 

0.06630 

10 

0.1340 

17,960 

14,103 

0-05435 

ii 

O.I20O 

14,400 

11,310 

0-04359 

12 

O.IOQO 

1  1,  880 

9,33i 

0.03596 

13 

0.0950 

9,025 

7,088 

0.02732 

14 

0.08300 

6,889 

5,4n 

0.02085 

15 

O.O72OO 

5,^84 

4,072 

0.01569 

16 

0.06500 

4,225 

3.3i8 

0.01279 

17 

0.0580 

3,364 

2,642 

0.01018 

18 

O.O4900 

2,401 

1,886 

0.007268 

iQ 

O.0420O 

1,764 

i,385 

0.005340 

20 

0.03500 

1,225 

962 

0.003708 

GAUGES   AND   MATERIALS 


11 


TABLE  OF  COMPARATIVE  SIZES  OF  WIRE  GAUGES,  IN 
DECIMALS  OF  AN  INCH 


No.  of 
Wire 
Gauge. 

Brown  & 
Sharpe. 

American 
Steel  &  Wire 
Co.  or 
Washburn 
&  Moen. 

Birmingham 
or  Stubb's. 

English 
Legal 
Standard. 

Old  English 
or  London. 

ooooooo 

O    4QOO 

o    <oo 

oooooo 

O.  58000 

w  .  £f.\yww 

o  d6i  ^ 

vx  -  Jv^v^ 

o  4.64. 

OOOQO 

0.51650 

w  »  -p  *  *  ^ 
o-4305 

0.500 

w.  -t  v  '-& 
0.432 



oooo 

000 
00 

o  .  46000 

0.40964 

0.36480 

0-3938 
0.3625 
0.3310 

0-454 
0.425 
0.380 

0.400 
0.372 
0.348 

0-454 
0.425 
0.380 

0 

I 

2 

0-32495 
0.28930 
0.25763 

0.3065 
0.2830 
0.2625 

0.340 
0.300 
0.284 

0.324 
0.300 
0.276 

0.340 
0.300 
0.284 

3 
4 
5 

0.22942 
0.20431 
0.18194 

0-2437 
0.2253 
0.2070 

0.259 
0.238 

0.220 

0.252 
0.232 

O.  212 

0.259 
0.238 

0.22O 

6 

7 
8 

0.16202 
o.  14428 
0.12849 

0.1920 
0.1770 
0.1620 

0.203 
0.180 
O.l65       • 

0.192 
0.176 

0.160 

0.203 
0.180 
0.165 

9 

10 

II 

0.11443 

0.10189 

0.09074 

0.1483 
0.1350 
0.1205 

0.148 

0.134 
0.120 

0.144 
0.128 
0.116 

0.148 

°-I34 

0.120 

12 
13 
14 

0.08081 

0.07196 
0.06408 

0-1055 
0-0915 
0.0800 

0.109 
0-095 
0.083 

0.104 
0.092 
0.080 

0.109 
0.095 
0.083 

15 

16 
i? 

0.05706 
0.05082 

0.04525 

0.0720 
0.0625 
0.0540 

0.072 
0.065 
0.058 

0.072 
0.064 
0.056 

O.O72 
0.065 
0.058 

18 
J9 

20 

0.04030 

0.03589 

0.03196 

0.0475 
0.0410 
0.0348 

0.049 
0.042 
0-035 

0.048 
0.040 
0.036 

0.049 
O.O4O 
0-035 

12 


ELECTRIC   POWER  CONDUCTORS 


TABLE  OF  COMPARATIVE  SIZES  WIRE  GAUGE,  IN    DECI- 
MALS OF   AN  INCH— Continued. 


No.  of 
Wire 
Gauge. 

Brown  & 
Sharpe. 

American 
Steel  &  Wire 
Co.  or 

Washburn 
&  Moen. 

Birmingham 
or  Stubb's. 

English 
Legal 
Standard. 

Old  English 
or  London. 

21 
22 

23 

0.02846 
0-02535 
0.02257 

0.03175 
0.0286 
0.0258 

0.032 
0.028 
0.025 

0.032 
0.028 
0.024 

0.0315 

0.0295 
0.0270 

24 

0.02OIO 

0.0230 

O.022 

0.022 

0.0250 

25 
26 

0.01790 
0.01594 

0.0204 
0.0181 

0.020 

0.018 

0.020 

0.018 

0.0230 
0.0205 

27 
28 

29 

O.OI42O 
0.01264 
O.OII26 

0.0173 
0.0162 
0.0150 

0.016 
0.014 
0.013 

0.0164 
0.0148 
0.0136 

0.01875 
0.01650 
.001550 

3° 

31 
32 

O.OI003 
0.00893 
0.00795 

0.0140 
0.0132  ' 
0.0128 

O.OI2 
0.010 
O.OO9 

0.0124 
0.0116 
0.0108 

0.01375 
0.01225 
0.01125 

33 
34 
35 

0.00708 
0.00630 
0.00561 

0.0118 
0.0104 
0.0095 

O.OO8 
0.007 
O.OO5 

0.0100 

0.0092 
0.0084 

0.01025 
0.00950 
o  .  00900 

36 
27 

O.OO5OO 

o  004.4.  ^ 

o  .  0090 
o  0085 

0.004 

0.0076 
0.0068 

0.00750 
0.00650 

"8 

o  00^96 

o  0080 

o  0060 

O.OO<TX. 

o° 
39 

AO 

0.00353 

o  oo  314 

0.0075 
o  0070 



0.0052 
o  0048 

0.00500 

o  00450 

The  Edison  Gauge  is  the  area  in  circular  mils  divided  by  one  thousand. 


3.  MECHANICAL    PROPERTIES   OF    CABLES 

The  terminology  relating  to  electric  cables  having 
evolved  out  of  that  used  for  ages  in  connection  with 
ordinary  rope,  is  unsatisfactory  and  indefinite.  It  is 


t 

GAUGES   AND   MATERIALS  13 

therefore  necessary  to  define  our  terms  before  con- 
sidering the  properties  of  electric  cables.  The  fol- 
lowing definitions  are  based  principally  on  common 
usage. 

Cable.  A  conductor  composed  of  a  number  of  wires 
twisted  together. 

Strand.  A  conductor  composed  of  a  straight  central 
wire  surrounded  by  one  or  more  layers  of  spirally 
laid  wires.  This  construction  is  frequently  called  a 
concentric  strand. 

Rope  Strand.  A  conductor  composed  of  a  straight 
central  strand  surrounded  by  one  or  more  layers  of 
spirally  laid  strands.  For  example,  a  rope-stranded 
cable  may  be  built  up  of  seven  strands,  each  strand 
of  nineteen  wires,  such  a  cable  is  briefly  described  as 
a  19X7  cable. 

Stranding  or  Laying.  The  process  or  method  of 
twisting  the  wires  or  strands  into  a  cable. 

Pitch.  The  length,  measured  along  the  cable  axis, 
of  a  complete  turn  of  a  strand  of  cable.  The  word 
lay  is  sometimes  used  instead  of  pitch.  Thus  the 
standard  pitch  recommended  by  the  British  Institution 
of  Electrical  Engineers  is  defined  as  "a  lay  of  twenty 
times  the  pitch  diameter." 

Pitch  Diameter.  The  diameter  of  the  spiral  made  by 
the  axis  of  a  wire  or  strand. 

The  following  definition  is  suggested  by  the  author: 

Pitch  Factor.  The  ratio  of  the  length  of  a  wire 
to  the  corresponding  axial  length  of  the  cable. 


14  ELECTRIC   POWER  CONDUCTORS 

If  D  =  pitch  diameter; 
P=  pitch;   then, 


,  Pitch  Factor  =  \  i  +    — 


Number  of  Wires  in  Cables.  Concentric-strand  cables 
are  made  up  of  7,  19,  37,  61,  91,  127,  etc.,  wires, 
the  numbers  being  obtainable  by  the  following  form- 
ula, in  which  n  is  the  number  of  layers  over  the 
core. 

The  number  of  wires  =  3  (n2  +  n)  +  i  . 

The  number  of  wires  per  layer  increases  by  six 
for  each  successive  layer;  thus,  the  first  layer  has  six, 
the  second  twelve,  the,  third  eighteen,  and  so  on. 

Rope-strand  cables  are  usually  made  of  strands 
composed  of  seven  wires  each.  The  number  of  strands 
in  such  a  cable  follows  the  same  law  as  the  number 
of  wires  in  a  concentric-strand  cable.  The  total  num- 
ber of  wires  therefore  follows  the  following  law: 

Core       =7. 

1  layer  =7X7. 

2  layers  -7  X  19. 

3  "      =7X37,  etc. 

n      "      = 


If  the  rope  is  made  up  of  strands  composed  of  any 
other  number  of  wires,  that  number  should  be  used 
in  the  place  of  the  seven  in  the  above  formula. 


GAUGES   ANP   MATERIALS 


15 


WIRES  IN  CONCENTRIC  CABLES 


Num- 
ber of 

Core  of  One 
Wire. 

Core  of  Two 
Wires. 

Core  of  Three 
Wires. 

Core  of  Four 
Wires. 

Layers 
over 
Core. 

Per 
Layer. 

Total. 

Per 
Layer. 

Total. 

Per 
Layer. 

Total. 

Per 
Layer. 

Total. 

I 

6 

7 

8 

10 

9 

12 

10 

14 

2 

12 

19 

U 

24 

15 

27 

16 

3° 

3 

18 

37 

20 

44 

21 

48 

22 

52 

4 

24 

61 

26 

70 

27 

75 

28 

80 

5 

3° 

9i 

32 

102 

33 

1  08 

34 

114 

6 

36 

127 

38 

140 

39 

M7 

40 

154 

Cables  having  more  than  one  wire  in  the  core  are  seldom  used. 
WIRES  IN  ROPE  CABLES 


Total  Number  of  Wires. 

Number  of 
Layers 
over  Core. 

Number  of 
Strands. 

7  Wires  per 
Strand. 

19  Wires  per 
Strand. 

37  Wires  per 
Strand. 

I 

7 

49 

133 

259 

2 

19 

133 

36t 

7°3 

3 

37 

259 

703 

1369 

4 

61 

427 

"59 

2257 

5 

9i 

637 

1729 

3367 

6 

127 

889 

2413 

4699 

Diameter  of  Cables.  It  being  standard  practice  to 
run  alternate  layers  in  opposite  directions,  the  wires 
cannot  fit  into  the  grooves  between  the  other  wires, 
and  the  total  diameter  is  therefore 


where  d  is  the  diameter  of  each  wire  or  strand,  and  n 
the  number  of  layers  over  the  core. 


16 


ELECTRIC   POWER  CONDUCTORS 


Thus  a  5  layer  91  wire  cable  composed  of  wires  of 
0.1048  in.  diameter,  has  a  total  diameter  of 

0.1048(1  +  10)  =1.1528  in. 

WEIGHT   OF   CABLES 


Number  of 
Layers. 

Wires  or  Strands 
in  Cable. 

Weight  of  Cable,  Lbs.  per  Foot. 

I 

7 

w(i  +  6pj 

2 

19 

iv(i  +  6pQ+i2pl2) 

n 

3(«2  +  «)  +  i 

w(i  +  6pQ+  i2/>12-f,  etc.) 

iv  =  weight  of  each  wire  or  strand,  Ibs.  per  foot; 
p6  =  pitch  factor  of  first  or  6  wire  layer; 
Pn  =  pitch  factor  of  second  or  12  wire  layer,  etc. 

(Definition  of  pitch  factor  on  page  13.) 

Pitch.  The  British  standard  pitch  is  twenty 
times  the  pitch  diameter,  and  is  the  only  standard 
pitch  agreed  upon  by  any  large  body  of  manufac- 
turers. In  America  there  is  no  standard  pitch,  this 
being  usually  left  to  the  manufacturers. 

The  cable  user  is  interested  in  obtaining  the  largest 
pitch  with  which  the  wires  will  hold  together  and 
that  obviously  depends  upon  the  size  and  number 
of  wires  and  upon  their  stiffness.  The  longer  the  pitch 
the  greater  the  conductance  and  tensile  strength. 

The  cable  manufacturers,  on  the  other  hand, 
generally  prefer  a  short  pitch.  The  pitch  to  be  used 
should  therefore  be  agreed  upon  by  manufacturers 
and  buyers  when  specifications  are  to  be  prepared. 
For  cables  of  hard-drawn  copper  for  aerial  lines,  a 


*  » 
GAUGES   AND   MATERIALS  17 

pitch  of  from  twenty  to  thirty-five  times  the  pitch 
diameter  is  usual  practice. 

Minimum  Pitch.  The  minimum  pitch  or  lay  with 
which  n  wires  of  diameter  d  can  be  coiled  spirally  on 
a  pitch  diameter  D,  is 

nD.nd 


)2-  (nd)2 

In  the  case  of  regular  concentric  cables  in  which 
successive  layers  have  6,  12,  18,  etc.,  wires,  the  mini- 
mum pitch  is  i  o.i  times  the  pitch  diameter  if  all  the 
wires  are  of  equal  size.  The  constant  10.1  equals 


Ultimate  Strength  of  a  Seven-Wire  Strand  with  Soft  Core. 

Let  p  =  pitch  factor  of  six- wire  layer; 

d  =  diameter  of  each  wire  (in.) ; 

t  =  tensile  strength  of  outer  wires,  Ibs.  per  sq.  n. ; 

e  =  elongation,  per  cent,  at  which  outer  wires 
break ; 

5  =  stress  in  Ibs.  per  sq.in.  in  core  with  elonga- 
tion e  (see  Fig.  2,  p.  7,  for  soft-drawn 
copper) . 

Ultimate  strength  (Ibs.)  =**&(s  +  -V 

4     \       p/ 

Ultimate  Strength  of  a  Nineteen-Wire  Strand  with  Soft  Core. 

Let  pQ  =  pitch  factor  of  six- wire  layer ; 
Pi2  =  pitch  factor  of  twelve- wire  layer; 
d  =  diameter  of  each  wire  (in.); 


18 


ELECTRIC   POWER  CONDUCTORS 


t  =  tensile  strength  of  outer  wires,  Ibs.  per 

sq.in.; 
e  =  elongation,  per  cent,  at  which  outer  wires 

break  ; 
5  =  stress,  Ibs.  per  sq.in.  in  core  with  elongation 

e  (Fig.  2,  p.  7,  for  soft-drawn  copper). 

Ultimate  strength  (Ibs.)  =-d2(s+  —  +  —  V 

4        \          PG       Pl2/ 

With    a  37-wire  strand,   the    bracketed  expression 
should  have  a  term   for  the    1  8-  wire   layer,   namely, 

18* 

—  ,  and  so  on,  for  all  sizes. 

PlB 

Space  Wasted  in  Concentric-Strand  Cables. 

n  =  number  of  concentric  layers  around  one  central 

wire; 
R  =  ratio  of  copper  area  to  area  of  circle  circum 

scribing  the  outside  of  cable; 
3( 


This  neglects   the   increase   of  ratio   due   to   wires 
being  arranged  in  spiral  form. 


Number  of 
Layers. 

Number  of 
Wires. 

R. 

_ 

I 

I.OOO 

I 

2 

7 
iQ 

0.778 

0.760 

3 

4 

37 
61 

0-755 
o-753 

5 

91 

0.752 

GAUGES   AND   MATERIALS 


19 


RESISTANCE  AND  WEIGHT  OF  STANDARD  BRITISH 
CABLES 


Wires  in  Cable. 

Ratio  of  Resistance  of  Cable, 
to  Resistance  of  One  Wire. 

Ratio  of  Weight  of  Cable, 
to  Weight  of  One  Wire. 

7 

0.14436 

7.0736 

J9 

0.05324 

19.2207 

37 
61 

0.02735 
0.01659 

37-4414 
6i-7356 

9i 

O.OIII2 

92.1034 

Based  upon  the  British  Institution  of  Electrical  Engineers'  Standard  of  a  lay  or 
pitch  of  twenty  times  the  pitch  diameter  which  corresponds  to  a  pitch  factor  of 
i. 01 22.  Both  the  weight  and  resistance  of  the  strand  are  about  one  per  cent  higher 
than  for  a  solid  wire  of  same  cross  section. 


DIAMETER  OF  WIRES  IN  STRANDS 


Size  of 


Number  of  Wires  in  Strand. 


Cable. 

7- 

19- 

37- 

61. 

91- 

127. 

Circ.  Mils. 

2,000,000 

0-5345 

0.3244 

0.2324 

0.1811 

0.1482 

o-i255 

1,750,000 

o.  5000 

0-3035 

0.2175 

0.1694 

0.1387 

0.1174 

1,500,000 

0.4629 

0.2810 

o.  2013 

0.1568 

0.1284 

0.1087 

1,250,000 

0.4226 

0.2565 

0.1838 

0.1431 

0.1173 

0.0992 

1,000,000 

°-3779 

0.2294 

0.1644 

0.1281 

0.1048 

0.0887 

750,000 

o-3273 

0.1986 

0.1428 

0.1109 

i  .  0908 

0.0769 

500,000 

0.2673 

o.  1622 

O.Il62 

0.0906 

0.0661 

0.0628 

250,000 

0.1889 

0.1147 

O.O822 

0.0640 

0.0524 

B.  &  S. 

0000 

o-i739 

0-1055 

0-07563 

0.0589 

000 

0.1548 

0.09398 

0.0674 

0.0525 

00 

0-1379 

o.  08369 

0.060 

0 

0.1228 

0.07453 

I 

0.1094 

0.06637 

2 

0.0974 

0.05911 

3 

0.0867 

4 

0.0772 

20 


ELECTRIC   POWER  CONDUCTORS 


DIMENSIONS  AND  WEIGHTS  OF  CABLES 
COPPER  AND  ALUMINUM 


Size. 

Number  of 
Wires  in 
Strand. 

Diameter  of 
Individual 
Wires  in 
Inches. 

Diameter  of 
Bare  Cables 
in  Inches. 

Approximate 
Weight  of 
Copper  per 
1000  Ft. 
in  Lbs. 

Approximate 
Weight  of 
Aluminum 
per  1000  Ft. 
in  Lbs. 

B.  &S. 

14 

7 

0.0243 

0.0729 

13 

3-87 

12 

7 

0.0306 

0.0918 

20 

5-95 

10 

7 

0.0386 

0.1158 

32 

9-54 

8 

7 

0.0485 

0-1455 

5* 

15-2 

6 

7 

o  .  06  i  3 

0.1839 

81 

24.1 

5 

7 

0.0688 

o.  2064 

1OI 

30.2 

4 

7 

0.0773 

0.2319 

128 

38-5 

3 

7 

0.0867 

o.  2604 

161 

48-5 

2 

7 

0.0974 

o.  2922 

203 

61 

I 

19 

0.0664 

0.3320 

256 

77 

O 

19 

0-0745 

0-375° 

323 

97 

00 

19 

0.0837 

0.4190 

408 

123 

000 

19 

.  0.094 

0.4700 

5U 

i55 

oooo 

19 

0.1055 

0.5280 

647 

i95 

CM. 

250,000 

37 

0.0822 

0-5754 

765 

239 

300,000 

37 

0.0906 

0.6342 

919 

276 

350,000 

37 

0.0974 

0.6818 

1070 

322 

400,000 

37 

0.104 

o.  7280 

T22O 

368 

450,000 

37 

O.III 

0.7770 

1380 

414 

500,000 

61 

0.0906 

0.8154 

1530 

460 

550,000 

61 

0.095 

0.8550 

J680 

506 

600,000 

61 

0.0992 

0.8928 

1840 

552 

650,000 

61 

0.1033 

0.9297 

1990 

597 

700,000 

61 

0.1072 

0.9648 

2140 

643 

750,000 

61 

0.1109 

0.9990 

2300 

690 

800,000 

61 

0.1146 

.031 

2450 

735 

900,000 

61 

0.1216 

.094 

2750 

834 

1,000,000 

61 

o.  1281 

-153 

3060 

920 

1,000,000 

oi 

0.1048 

-153 

3°3° 

924 

1,250,000 

91 

0.1173 

.290 

3830 

1150 

1,500,000 

9i 

0.1284 

.412 

4590 

1380 

1,750,000 

127 

0.1174 

.526 

536o 

1610 

2,000,000 

127 

°-T255 

-631 

6120 

1840 

2,000.000* 

133 

0.1226 

-84 

6220 

1850 

Rope. 


GAUGES   AND   MATERIALS  21 

The  above  figures  should  be  regarded  as  approxi- 
mate only,  as  the  cable  diameters  and  weights  de- 
pend upon  the  pitch  of  the  spirals. 

An  allowance  of  i%  is  made  for  increase  of  weight 
due  to  spiralling. 

The  size  of  area  is  based  upon  the  united  areas 
of  the  individual  wires  cut  at  right  angles  to  their 
axes  and  laid  out  straight. 


CHAPTER  II 
ELECTRICAL    PROPERTIES  '  OF    CONDUCTORS 

i.  RESISTANCE  OF  WIRES  AND  CABLES 

MATTHIESSEN'S   STANDARD 

The  recognized  standard  of  conductivity  of  copper 
wire  is  that  established  by  Matthiessen,  from  experi- 
ments on  pure  copper.  Matthiessen's  standard  for 
soft-drawn  copper  is  that  a  wire  one  meter  long,  of 
uniform  cross-section,  weighing  one  gram,  has  a 
resistance  of  0.141729  ohm  at  o°  C. 

While  Matthiessen's  standard  is  often  reached 
and  even  exceeded  in  commercial  copper,  it  is  usual 
to  accept  soft-drawn  copper  having  98%  and  hard- 
drawn  copper  having  97%  of  the  above  standard 
conductivity. 

Matthiessen's  special  standard  for  hard-drawn 
copper  is  not  used  in  America. 

The  conductivity  of  aluminum  is  from  55%  to 
63%  of  Matthiessen's  standard  for  copper,  the  usual 
commercial  figure  being  62%,  which  is  equivalent 
to  15.47  ohms  per  mil-foot  at  o°  C. 

22 


ELECTRICAL   PROPERTIES   OF  CONDUCTORS  23 


The  variation  of  resistance  with  temperature,  both 
for  copper  and  aluminum,  is  about  0.42%  per  degree 
Centigrade  or  0.23%  per  degree  Fahrenheit. 

RESISTANCE   OF  A   MIL-FOOT   OF   COPPER,    OHMS 

(One  circular  mil  area,  i  foot  long.) 


Temperature  Degrees. 

Per  Cent  Conductivity  —  Matthiessen. 

Cent. 

Fahr. 

100. 

99- 

98. 

97- 

96. 

0 

32 

9-59 

9.69 

9-79 

9.89 

9-99 

10 
15-5 

5° 
60 

9-99 

10.2 

10.  I 
10.3 

IO.  2 
10.4 

10.3 

i°-5 

10.4 
10.6 

2O 
24 
30 

68 

75-2 
86 

10.4 

10.6 
10.8 

io-5 
10.7 
10.9 

10.6 
10.8 

II.  0 

10.7 
10  9 
ii.  i 

10.8 

II.  0 
II.  2 

40 

SO 
60 

104 

122 
140 

II.  2 

ii.  6 

12.0 

"•3 
11.7 

12.  I 

II.  4 

ii.  8 

12.2 

n-5 

12.0 
12.4 

II.7 
12.  I 

12-5 

70 
80 
90 

158 
I76 
194 

12.4 
12.8 
13.2 

12.5 

12.9 
13-4 

I2.7 
I3-I 
13-5 

12.8 
13.2 
13-6 

I2.9 
13-3 
I3-» 

100 

212 

13-6 

13-7 

13-9 

14.0 

14.2 

Based  on  Matthiessen's  Standard,  9.5916  ohms  per  mil-foot  at  e°  C.  and  the 
A.A.I. E  E.  temperature  coefficient,  0.0042  from  o°  C. 

For  any  other  percentage  conductivity  divide  the 
number  in  the  column  headed  100  by  the  conductivity 
expressed  as  a  decimal  fraction.  For  example,  the 
ohms  per  mil-foot  for  aluminum  of  62%  conductivity  at 

70°  C.  is  -   —  =  20.0. 
0.62 


24 


ELECTRIC   POWER  CONDUCTORS 


ii.U 

109 

,/ 

/ 

in  R 

I 

\f/ 

107 

il. 

I 

10  fi 

/ 

7; 

/ 

105 

/ 

/ 

104 

/J 

/ 

.  if)  q 

/ 

/ 

8m2 

/, 

/ 

^  101 

/ 

/ 

10.0 

/ 

/ 

o  q 

/ 

7 

98 

/ 

/ 

97 

/ 

G 

t 

q  « 

/ 

/ 

9.5 

/ 

/ 

0         10         20        30        40        50        60        70        80        90        100 
Degrees  Fahrenheit 

FIG.  3. — Resistance  of  Copper.      Based  on  Standards  adopted  by  A.I.E.E. 


ELECTRICAL  PROPERTIES   OF  CONDUCTORS  25 


RESISTANCE  OF  SOLID   COPPER  WIRE 
CONDUCTIVITY  100  PER  CENT — MATTHIESSEN'S  STANDARD 

Ohms  per  1000  Feet. 


Size. 

o°C. 
32°  F. 

10°  C. 
50°  F. 

20°  C. 

68°  F. 

So°  C. 

122°  F. 

Millions 

of  C.M. 

5 

0.001918 

0.001999 

0.002079 

O.OO232I 

4 

0.002398 

0.002499 

0.002599 

0.002901 

3 

0.003197 

0.003331 

0.003466 

0.003869 

2 

0.004796 

0.004997 

0.005199 

0.005803 

If 

0.005481 

0.005711 

0.005941 

O.OO6632 

l£ 

0.006394 

0.006663 

0.006932 

0-007737 

ii 

0.007673 

0.007996 

0.008318 

O.O09285 

i 

0.009592 

0.009994 

0.01040 

o.  01161 

f 

0.01279 

0.01333 

0.01386 

0.01547 

i 

0.01918 

0.01999 

0.02079 

0.02321 

I 

0-03837 

0.03998 

0.04159 

0.04642 

B.  &S. 

oooo 

0.04528 

0.04718 

0.04909 

0.05479 

000 

0.05716 

0.05956 

0.06196 

0.06916 

00 

0.07207 

0.07510 

0.07813 

0.08721 

0 

0.09089 

0.09470 

0.09852 

O.IIOO 

i 

0.1146 

0.1194 

0.1242 

0.1387 

2 

0-1445 

0.1506 

0.1566 

0.1749 

3 

0.1822 

0.1899 

0-1975 

0.2205 

4 

0.2298 

0.2394 

0.2491 

0.2780 

5 

0.2898 

0.3019 

0.3141 

0.3506 

6 

0-3654 

0.3807 

0.3961 

0.4421 

7 

0.4608 

0.4801 

0.4995 

o-5575 

8 

0.5810 

0.6054 

0.6297 

0.7029 

9 

0.7325 

0-7633 

0.7941 

0.8863 

10 

0.9239 

0.9627 

I.OOI 

1.118 

1  1 

1.165 

1.214 

1.263 

1.410 

12 

1.469 

I-53T 

1.592 

1.777 

13 

1.852 

1.930 

2.008 

2.241 

14 

2-335 

2-434 

2.532 

2.826 

15 

2-945 

3.069 

3.192 

3-563 

16 

3-713 

3.869 

4-025 

4-493 

17 

4.683 

4.880 

5-077 

5-667 

18 

5.906 

6-154 

6.402 

7.146 

Based  upon  Matthiessen's  Standard  of  9-S9i6  ohms  per  mil-foot  at  o°  C.  and  the 
A.I.E.E.  temperature  coefficient  of  0.0042  per  degree  Centigrade  temperature  rise 
above  o°  C. 

Resistance  at  t°  C.  is  equal  to  that  at  zero  multiplied  by  (i  +0.00420. 


26 


ELECTRIC   POWER  CONDUCTORS 


RESISTANCE  OF  SOLID   COPPER  WIRE 

CONDUCTIVITY  98  PER  CENT — MATTHIESSEN'S  STANDAKD 

Ohms  per  1000  Feet. 


Size. 

o°C. 
32°  F. 

10°  C. 
50°  F. 

20°  C. 

68°  F. 

So°  C. 

122°  F. 

Millions 

of  C.M 

5 

0.001957 

0.002040 

O.OO2122 

O.OO2369 

4 

0.002447 

0.002550 

0.002652 

0.00296l 

3 

0.003262 

0.003400 

0.003536 

0.003948 

2 

0.004894 

0.005099 

0.005305 

0.005921 

If 

0-005593 

0.005828 

0.006063 

0.006767 

I* 

0.006525 

0.006799 

0.007073 

0.007895 

Ij 

0.007830 

0.008159 

0.008488 

0.009474 

I 

0.009787 

0.01020 

o.  01061 

O.OII84 

I 

0.01305 

0.01360 

O.OI4I5 

0-01579 

J 

0.01957 

0.02O4O 

0.02122 

0.02369 

J 

0.03915 

0.04079 

'0.04244 

0-04737 

B.  &  S. 

0000 

0.04621 

,    O.04820 

0.05009 

0-05597 

ooo 

0-05833 

0.06078 

0.06323 

0.07057 

oo 

o-o7355 

0.07663 

0.07972 

0.08899 

0 

0.09274 

0.09664 

0.1005 

O.II22 

I 

0.1169 

O.I2I9 

0.1268 

0.1415 

2 

0.1475 

0-1537 

0.1598 

0.1784 

3 

0.1860 

0.1938 

0.2016 

0.225O 

4 

0-2345 

0.2443 

0.2542 

0.2837 

5 

0.2957 

0.3081 

0.3205 

0-3578 

6 

0.3728 

0.3885 

0.4042 

0.45II 

7 

0.4702 

0.4899 

0.5097 

0.5689 

8 

0.5928 

0.6177 

0.6426 

0-7173 

9 

0-7475 

0.7789 

0.8103 

0.9044 

10 

0.9427 

0.9823 

1.022 

I.I4I 

ii 

1.189 

I  .  238 

1.288 

1.438 

12 

i-499 

1.562 

1.625 

I.8I4 

13 

1.890 

1.970 

2.049 

2.287 

14 

2-383 

2.483 

2.583 

2.884 

15 

3-o°5 

3-I31 

3-257 

3-636 

16 

3-789 

3-948 

4-107 

4-585 

i7 

4-779 

4.980 

5.180 

5-783 

18 

6.027 

6.280 

6-533 

7.292 

Based  upon  Matthies?en's  Standard  of  9.5916  ohms  per  mil-foot  at  o°  C.  and  the 
A.I.E.E.  temperature  coefficient  of  0.0042  per  degree  Centigrade  temperature  rise 
above  o°  C. 

Resistance  at  t°  C.  is  equal  to  that  at  zero  multiplied  by  (i  +0.0042*). 


ELECTRICAL  PROPERTIES  ~OF  CONDUCTORS  27 


RESISTANCE   OF  ALUMINUM   WIRE 

CONDUCTIVITY  62  PER  CENT — MATTHIESSEN'S  STANDARD 
Ohms  per  1000  Feet. 


Size. 

o°C. 
32°  P. 

10°  C. 

50°  F. 

2C°  C. 

68°  F. 

50°  C. 

122°  F. 

Millions 

of  C.M. 

5 

.003094 

.003224 

-003354 

.003744 

4 

.003868 

.  004030 

.004192 

.  004680 

3 

-005157 

-005373 

-005590 

.006239 

2 

-007735 

.008060 

.008385 

.  009360 

l| 

.008840 

.009211 

.009583 

.01070 

I* 

.01031 

.01075 

.01118 

.01248 

I* 

.01238 

.01290 

.01342 

.01497 

I 

-01547 

.Ol6l2 

.01677 

.01872 

1 

.02063 

.02149 

.02236 

.02496 

* 

.03094 

.03224 

-03354 

.03744 

i 

.06188 

.06448 

.06708 

.07488 

B  &  S. 

0000 

-07304 

.07610 

.07917 

.08837 

000 

.09219 

.  09606 

.09994 

.1116 

00 

.1162 

.1211 

.1260 

.1407 

0 

.1466 

.1527 

.1589 

-1774 

I 

.1848 

.1926 

.2004 

-2237 

2 

-2331 

.2429 

-2527 

.2820 

3 

-2939 

-3063 

.3186 

-3556 

4 

.3706 

.3862 

-4017 

.4484 

5 

.4674 

.4870 

-5066 

-5655 

6 

.5893 

.6141 

.6388 

-7131 

7 

-7432 

-7744 

.8056 

.8992 

8 

-937° 

.9764 

1.016 

1.134 

9 

1.181 

I.23I 

1.281 

1.430 

10 

1.490 

i-553 

1.615 

1.803 

ii 

1.879 

1.958 

2.037 

2.273 

12 

2.369 

2.469 

2.568 

2.867 

»3 

2.988 

3-"3 

3-239 

3-615 

14 

3-767 

3-925 

4-083 

4.558 

15 

4-750 

4-949 

5-149 

5-747 

16 

5-989 

6.241 

6.492 

7-247 

i7 

7-554 

7.871 

8.188 

9.140 

18 

9.526 

9.926 

io-33 

u-53 

Based  upon  Mathiessen's  Standard  of  9.516  ohms  per  mil-foot  at  o°  C.  and 
the  temperature  coefficient  of  0.0042  per  degree  Centigrade  temperature  rise 
above  o°  C. 

Resistance  at  t°  C.  is  equal  to  that  at  zero  multiplied  by  (i  +  .oo42/). 


28  ELECTRIC   POWER  CONDUCTORS 

The  following  rules,  which  are  easily  remembered, 
enable  one  to  determine  approximately  the  constants 
of  any  size  of  copper  or  aluminum  wire  on  the  B.  &  S. 
gauge  without  reference  to  a  wire  table. 

1.  A  No.  10  copper  wire  has  a  resistance  of  approxi- 
mately one  ohm  per  1000  feet,  a  cross  section  of  10,000 
C.M.  and  weight  of  32  Ibs.  per  1000  ft. 

2.  A   No.    10   aluminum  wire  has  a  resistance  of 
approximately  1.6  ohms  per  1000  feet,  a  cross  section 
of  10,000  C.M.  and  weights  9.5  per  1000  feet. 

3.  An  increase  of  one  in  the  number  of  a  wire  in- 
creases the  resistance  25  per  cent;   an  increase  of  two 
in  the  number  increases  the  resistance  60  per  cent ;  an 
increase  of  three  in  the  number  doubles  the  resistance 
an  increase  of  ten  in  the  number  increases  the  resist- 
ance ten  times. 

4.  The  cross  section  and  weight  of  a  wire  varies  in- 
versely as  the  resistance ;  the  diameter  in  mils  is  equal 
to  the  square  root  of  the  cross  section  in  circular  mils 
(a  stranded  wire  has  a  diameter  about  15  per  cent 
greater) . 

Examples:  The  resistance  of  a  number  18  copper 
wire  is  4  X  1.60  =  6.4  ohms  per  thousand  feet;  the  cross 

10,000  / 

section  is =  i  560  C.M. ;  the  diameter  is  v  1 560 

6.4 

=  39.5  mils;  the  weight  —  =5.00   Ibs.  per  1000  feet. 

6.4 

The  resistance  of  a  number   oo  stranded  aluminum 

wire  is : =  0.128  ohms  per  1000  feet;  the  cross 

10X1.25 


ELECTRICAL   PROPERTIES   OF  CONDUCTORS  29 

section    —    -X  10,000  =  125,000    C.M. ;    the    diameter 

O.I2O 

1.6 


1.15^/125,000  =  406  mils;  the  weight  -    — X9-5  =  ii9 

Ibs.  per  1000  feet. 

Increase  of  Resistance  Due  to  Spiralling.  The  area 
of  a  cable  for  electrical  purposes  is  taken  to  be 
the  sum  of  the  areas  of  the  wires  when  laid  out 
straight  and  measured  in  a  plane  at  right  angles 
to  their  axes.  Hence,  calculating  the  resistance  of 
a  cable  accurately  we  must  take  into  account  the 
increase  in  effective  length  due  to  spiralling. 
Let  a  =  area  of  each  wire  in  circular  mils. 

k  =  resistivity  of    the  wires   in  ohms  per  mil- 
foot. 

PQ  =  pitch  factor  of  layer  of  6  wires. 
piz=  pitch  factor  of  layer  of  12  wires,  etc. 
The  resistance  of  a  seven-wire  cable  equals 

k      fin 

ohms  per  foot. 
a  "  '  " 


The  actual  path  of  the  current  is  along  the  spiral, 
a  very  small  proportion  passing  from  wire  to  wire. 

Formulae  for  larger  cables  are  cumbersome,  but 
calculations  may  be  made  by  considering  the  layers 
individually  and  grouping  them  in  multiple.  The 
proper  value  of  p  for  each  layer  being  assumed,  we 
have  the  following  resistances. 


30 


ELECTRIC   POWER  CONDUCTORS 


Wires  in  Layer. 

Resistance  of  Each 
Layer,  Ohms. 

I 

k 
a 

6 

£•* 

12 

~\2a  '  ^^ 

18 

A.#a 

etc. 

etc. 

n 

k 

na 

See  p.  19  for  Resistance  of  Standard  British  Cables,  for  which  the  pitch  is  twenty 
times  the  diameter. 


VARIATION   OF   RESISTANCE   WITH   TEMPERATURE 

All  materials  suffer  a  slight  increase  of  resistance 
with  rise  of  temperature.  For  all  pure  metals  except 
iron  and  nickel,  this  amounts  to  about  two-fifths  of  one 
per  cent  per  degree  Centigrade.  Iron  and  nickel  show 
an  increase  of  .005  and  .007  respectively. 

The  law  of  increase  of  resistance,  although  for  most 
purposes  proportional,  is  not  always  exactly  so,  and 
depends  not  only  on  the  metal  but  also  on  the  physical 
condition  of  the  sample  experimented  on. 

Measurements  by  Kennelly  and  Fessenden  appear  to 
show  that  the  resistance  of  commercial  copper  follows 
a  straight-line  law,  that  is,  the  equation  connecting 
resistance  and  temperature  is  of  the  form, 


R=r(i+at), 


- 
ELECTRICAL   PROPERTIES   OF  CONDUCTORS  31 

where  R  -resistance  at  t°  Cent. ; 
r=  resistance  at  o°  Cent. 

The  coefficient  a  appears  to  depend  on  the  quality 
of  the  sample.  The  following  values  are  used: 

Authority.  Coefficient  a. 

American  Institute  of  Electrical  Engineers 
Standardization  Report,  value  used  in  U. 
S.  A.  and  accepted  by  American  Authorities 

as  correct 0042 

British  Engineering  Standards  Committee 00428 

German 0040 

Matthiessen  (Phil.  Transac.  1862)  gave  the  follow- 
ing formula,  which  was  used  in  making  up  the  Ameri- 
can Institute  of  Electrical  Engineers'  Wire  Table: 

Ct  =  conductivity  at  t°  C. 
C0  =  conductivity  at  o°  C.; 

Ct  =  Co(l  —  .O03,89O,I/  +  .OOO,OOQ,OO9/2). 

The  second  significant  figure  being  doubtful,  the 
absurdity  of  having  five  is  apparent.  The  reciprocal 
formula  is  in  the  form  of  a  convergent  series  and  is 
unwieldy.  The  following  widely  published  formula  is 
obtained  by  omitting  the  terms  containing  the  higher 
powers  of  t  than  t2: 

R  =r(i  +  .00387^  +  .000, 005, 968/2). 

It  was  pointed  out  by  F.  B.  Crocker  (Elect.   World, 
Feb.  23,  1907),  that  the  higher  terms  are  not  negligi- 


32  ELECTRIC   POWER  CONDUCTORS 

ble  and  that  an  error  of  over  1.7%  is  obtained  at  100°  C. 
The  following  approximation  is  more  nearly  correct: 

R=r(i  +  .004/  +  . 000,002, 4/2). 

The  error  at  100°  C.  is  only  i/io  of  i%  compared  with 
Matthiessen's  formula.  Professor  Crocker,  in  the 
article  above  referred  to,  says  that  "the  formula 
adopted  in  the  A.  I.  E.  E.  Standardization  Report  is 
probably  as  nearly  correct  as  any  general  expression 
can  be  made." 

The  author's  concurrence  with  this  statement  led  him 
to  calculate  new  wire  tables  to  supersede  that  of  the  A. 
I.  E.  E.,  these  tables  being  given  on  pages  25  and  26. 

The  temperature  coefficient  of  aluminum  is  practi- 
cally the  same  as  that  of  copper,  but  is  sometimes 
given  as  .00423  per  degree  Centigrade. 

Temperature  -  Resistance  Calculations  for  Copper. 
Slide-rule  Method.  The  following  method  is  of  great 
value  on  account  of  its  simplicity,  but  requires  a 
slide  rule  marked  as  described  below. 

Mark  slide  (lower  scale)  as  follows : 

Slide  Rule  Number.  Marking  of  New  Scale. 

238  o 

248  10 

258  20 

268  30 

278  40 

288  5° 

298  60 

308  7° 

318  80 

328  90 

338  100 

etc.  etc. 


ELECTRICAL   PROPERTIES   OF  CONDUCTORS  33 

Example  showing  how  to  use  temperature  scale: 
Suppose  a  copper  wire  to  have  a  resistance  of  300 
ohms  at  13°  C.,  what  will  be  its  resistance  at  100°  C.  ? 

Set  13  on  the  new  slide  scale  opposite  300  on  the 
lower  scale  and  read  on  the  lower  scale  the  desired 
resistance  404  opposite  100  on  the  new7  scale. 

This  method  is  based  on  the  coefficient  0.0042 
adopted  by  the  American  Institute  of  Electrical  En- 
gineers, using  the  formula 


238 

(H.  Fender,  Elect.  World,  New  York,  April  13,  1907). 

2.  RESISTANCE    OF    NETWORKS    OF   CONDUCTORS 

KIRSCHOFF'S   LAWS 

(1)  In  any  branching  network  of  wires,  the  alge- 
braic sum  of  the  currents  in  all  the  wires  that  meet 
in  any  point,  is  zero. 

(2)  When    there    are   several    electromotive    forces 
acting  at  different  points  of  a  circuit,  the  total  elec- 
tromotive force  around  the  circuit  is   equal   to   the 
sum  of  the  resistances  of  its  separate  parts   multi- 
plied   each    into    the    strength    of    the    current    that 
flows  through  it. 

Maxwell's  Imaginary  Currents.  In  any  network  of 
conductors  it  is  permissible,  for  purposes  of  calcu- 
lation, to  replace  the  actual  currents  through  the 
network,  by  imaginary  currents  flowing  in  the 


34 


ELECTRIC   POWER  CONDUCTORS 


closed  cricuits  formed  by  each  mesh.  These  imagi- 
nary currents  are  taken  as  circulating  in  one  direc- 
tion, say  the  clockwise  direction,  and  are  all  given 
the  same  sign,  say  the  positive.  Should  it  be  con- 
venient, for  any  reason,  to  take  a  current  flowing 
in  the  opposite  direction,  it  should  be  given  a 
negative  sign.  In  each  mesh  the  sum  of  the  IR 
drops  equals  the  E.M.F.  in  the  mesh,  this  being 
zero  unless  there  is  a  generator.  If  the  generator 
E.M.F.  is  in  the  same  direction  as  the  current, 
the  E.M.F.  is  positive;  if  it  opposes  the  imaginary 
current,  its  sign  is  negative. 

Example.  Let  a,  6,  c,  d,  e,  f,  g,  h,  and  i  be  the 
resistances  of  the  various  branches  of  the  network 
represented  in  Fig.  4,  and  w,  x,  y,  and  z  the  imaginary 


currents  in  the  various  meshes  as  shown,  the  direc- 
tion of  each  current  being  assumed  to  be  clockwise. 
The  only  E.M.F.  in  the  system  is  E,  produced  by  a 
battery  in  the  branch  i.  Then, 


ELECTRICAL   PROPERTIES   OF  CONDUCTORS  35 


+  c)-Yg-Ze-Wc=o', 
Y(g  +  b  +  d+f)-Xg-  Zf-Wd^o 
Z(e+f+h)-Xe-Yf-Wh        =o; 
+  h  +  d)-Xc-Yd-Zh=E. 


Rearrange  the  equations  so  as  to  make  them  all 
of  the  same  form;  thus, 


-Yg-Ze  =o; 

Wd-Xg  +  Y(g  +  b  +  d+f)-Zf=o; 

-Wh-Xe  -Yf+Z(e+f+h)        =o; 

+  d)-Xc-Yd-Zh  =E. 


These   equations   may   be   solved   in   the   ordinary 
way  or  by  determinants,  as  described  below. 


SOLUTION    OF   EQUATIONS   BY  DETERMINANTS 

In  order  to  solve  such  a  series  of  equations  the 
following  pair  of  "  determinants  "  are  written  out: 


W  = 


o          (a  - 

\-g  +  e  + 

c)           -g                   -e 

0 

-g 

(g  +  b  +  d+f)           -c 

0 

—  e 

-f         (e+f+h) 

E 

c 

-g                  -h 

—  c         (a- 

f-£  +  ^  + 

c)           -g                  -e 

-d 

Q 

(g  +  b  +  d+f)           -c 

-h 

—  e 

-f         (e+f+h) 

(i  +  c  +  h  +  d) 

—  c 

-g                  -h 

36.  ELECTRIC   POWER  CONDUCTORS 

In  the  above  equation  it  should  be  noted  that  the 
denominator  consists  of  the  terms  of  -the  four  equa- 
tions with  the  W,  X,  Y  and  Z  omitted.  The  numera- 
tor differs  from  the  denominator  only  in  that  the 
column  of  W  terms  is  replaced  by  the  terms  on  the 
right-hand  side  of  the  four  equations.  Were  X  the 
unknown,  the  second  column  of  the  numerator  would 
be  replaced  by  the  terms,  o,  o,  o,  and  E. 

The  numerator  and  denominator  of  the  above 
equation,  each  constitute  what  is  called  a  determi- 
nant, and  are  simplified  by  the  following  rules.  When 
the  value  of  W  has  been  found,  the  resistance  of 

the  circuit  external  to  the  generator  is  •— . 

Rules,  (i)  If  a  determinant  has  two  equal  rows  or 
columns,  it  is  equal  to  zero. 

(2)  To  any  row  or  column  it  is  possible  to  add 
or  subtract  any  number  of  times  any  other  row  or 
column  without  altering  the  value  of  the  determinant. 

(3)  To  multiply  any  row  or  column  by  a  number 
is  equivalent  to  multiplying  the  whole  determinant 
by  that  number. 

(4)  If  all  the  terms  in  a  row  or  column  except 
one  are  zero,   the  determinant  reduces  to  one  of  a 
lower  order  which  may  be  obtained  by  striking  out 
the  row  and  column  which  intersect  at  the  term  in 
question,   and  multiplying  the  whole  by  that  term, 
the   sign   of   the   determinant   being   settled   in    the 
following  way: 


ELECTRICAL   PROPERTIES   OF  CONDUCTORS    37 

The  line  of  terms  beginning  at  the  upper  left-hand 
corner  and  ending  at  the  lower  right-hand  corner, 
is  called  the  principal  diagonal  of  the  determinant. 
If  the  uncancelled  term  in  the  line  of  zeros  is  on  the 
principal  diagonal  or  is  removed  from  it  by  an  even 
number  of  terms,  the  term  by  which  the  determi- 
nant is  multiplied  in  lowering  its  order,  is  positive. 
If,  however,  this  term  is  removed  from  the  principal 
diagonal  by  an  odd  number  of  terms,  the  multiply- 
ing terms  is  negative.  Thus, 


and 


I 

5 

6 

3 

I 

6 

3 

2 

i 

I 

5 

2 

i 

5 

=  2 

4 

3 

2 

1 

4 

2 

i 

o 

2 

0 

0 

I 

5 

6 

3 

I 

5 

3 

o 

i 

i 

5 

ry 

2 

i 

5 

4 

3 

2 

i 

4 

3 

i 

0 

0 

2 

0 

the  principal  diagonal  being  that  with  the  figures  :«, 
2,  and  o.  It  is  immaterial  whether  the  distance 
from  the  diagonal  is  counted  along  a  row  or  a  column. 
(5)  A  determinant  of  the  second  order  is  ex- 
panded in  the  following  way 


The  reduction  of  determinants  is  effected  by  alter- 
ing the  terms  according  to  the  above  rules  until  a 


38 


ELECTRIC   POWER  CONDUCTORS 


row  or  column  is  obtained  in  which  all  terms  but 
one  are  zero.  This  enables  a  reduction  or  order  to 
be  effected  in  accordance  with  rule  4.  Reductions 
are  continued  until  one  of  the  second  order  is 
obtained. 
Example  i. 

x+   y+   3  =  6; 


Then 


6  i  i 
8  2  i 
g  i  2 


III 

121 
I        12 


0          0 

i 

2            I 

i 

~3    -i 

2 

I        I 

0 

I           2 

O 

I            I 

I 

2 

I 

-3 

-  I 

i 

I 

i 

2 

I  _ 

I 

In  the  numerator,  the  following  steps  were  taken. 
Six  times  the  last  column  was  subtracted  from  the 
first,  and  the  last  column  was  subtracted  from  the 
second.  In  the  denominator,  the  first  column  was 
subtracted  from  the  last.  The  determinants  were 


ELECTRICAL   PROPERTIES   OF  CONDUCTORS    39 


then   reduced   to   the   second   order    bv   rule   4, 
expanded  by  rule  5. 
Similarly, 


and 


i  6   i 

100 

i  8   i 

120 

2    0 

192 

i  3   i 

3   i 

iii 

I    I    0 

I    I 

121 

120 

I    2 

112 

III 

=  2 


Hence  2  =  3,  by  subtraction. 

Actual  cases  are  usually  worked  out  without 
copying  the  various  steps  of  the  determinant,  the 
changes  being  made  with  pencil  and  eraser. 

Example  2.     Reduce  the  following  determinant. 
2     4     7 

2  5     8 

3  8     9 

Subtract    twice    the    first   column   from    the   second, 
and  \  of  the  first  column  from  the  third. 


21  I 

3        2         -f 

Reducing  to  the  second  order— 


Expanding— 


40  ELECTRIC   POWER  CONDUCTORS 

3.    RESISTANCE    TO    ALTERNATING    CURRENTS    OR 
SKIN    EFFECT 

NATURE   OF   SKIN  EFFECT 

THE  current  induced  in  a  conductor  begins  at 
the  surface  and  rapidly  diffuses  inward.  When  an 
alternating  E.M.F.  is  applied,  the  current  started 
by  a  positive  impulse  has  only  time  to  diffuse  a 
short  distance  from  the  surface  before  the  succeed- 
ing impulse  starts  an  opposite  current  from  the 
surface.  The  effect  is  that  the  current  never  attains 
its  full  value.  A  conductor  therefore  offers  greater 
resistance  to  alternating  than  to  direct  current. 

Calculation  of  Skin  Effect  for  a  Cylindrical  Wire.     Let 
R  =  ratio  of  alternating  current  resistance  to   direct 

current  resistance. 

M  =  area  of  conductor,   circular  mils. 
N  =  cycles  per  second. 
jj.  =  permeability  of  conductor. 

k  =  resistance    of    a    mil-foot   of    the    conductor    at 
the  temperature  under  consideration. 


= 


The  relation  between  R   and  Z  is   given  by  the 
curve  of  Fig.  5,  and  by  the  following  table. 

TABLE  I 

APPROXIMATE  VALUE   OF  R 
Z  less  than  i.  4  R=i 

Z  between  1.4  and  4.0  R  is  as  given  in  Table  II 

Z  is  greater  than  4.0  R=o.^4Z-\-  0.24 


ELECTRICAL    PROPERTIES   OF  CONDUCTORS    41 


3.0 
R 
2.0 

1.0 
( 

x 

^ 

™ 

/ 

X 

X 

x^ 

/ 

/ 

/ 

> 

/ 

/ 

/ 

/ 

/ 

s 

s 

2 

X 

^^ 

) 

1      — 
1 

.  —  • 
2 

3 

4       Z       5 
FIG.  5. 

TABLE  II 

6 

7 

8 

9 

z. 

R. 

Z. 

R. 

1.48 

I.  01 

2.80 

1.16 

1.64 

1.02 

2.84 

1.17 

1.78 

1.03 

2.89 

1.18 

1.90 

1.04 

2-94 

1.19 

2.OO 

1-05 

2-99 

i.  20 

2.  II 

I.  06 

3-°3 

I.  21 

2.  2O 

1.07 

3-o8 

1.22 

2.28 

I.  08 

3.12 

1.23 

2.36 

1.09 

3-i4 

1.24 

2-43 

I.JO 

3-20 

J-25 

2.50 

I.  II 

3-24 

1.26 

2.57 

I.  12 

3-27 

1.27 

2-63 

I-I3 

3-3i 

1.28 

2.68 

I.I4 

3-34 

1.29 

2-74 

I-I5 

3-38 

1.30 

42 


ELECTRIC   POWER  CONDUCTORS 


The  calculation  of  skin-effect  in  copper  and  other 
non-magnetic  conductors  presents  no  difficulties 
because  /*  is  unity.  In  the  case  of  iron  and  other 
magnetic  metals,  calculation  is  rendered  difficult  by 
the  necessity  of  using  the  proper  value  of  /£  which 
depends  on  the  current.  The  following  table  gives 
the  results  of  tests  by  L.  Lichens tein.  (Electrician, 
London,  Aug.  23,  1907.) 

TEST  ON  RAIL 


Cycles  per 
Second. 

Amperes. 

A.C.  Resistance. 

Equivalent  /-*. 

D.C.  Resistance. 

58-5 

49 

4-34 

8.0 

48.7 

153-8 

5-55 

7-2 

Rail 

28.2 

62.5 

2-85 

14.8 

bonded 

25-4 

108.4 

3-76 

15.0 

with 

19.4 

36-4 

2-5 

16.0 

copper 

17-3 

123.2 

2-93 

i9-3 

58.6 

35 

2.68 

9.6  ] 

48.6 

152 

3-42 

r        not 

28.4 

25-7 

46.2 
169 

i-94 

2.2 

II.  0     |     ,      ' 

14.4  J  bonded 

Area  of  rail,  5160  sq.mrn.  =  8  sq.in. 


LARGE   CABLES   ON   A.C.   CIRCUITS 

Owing  to  the  fact  that  alternating  current  flowing 
in  large  cables  has  greater  density  on  the  surface 
of  the  conductor  than  in  the  center  (so-called  skin 
effect),  an  ordinary  cable  will  not  carry  as  much 
alternating  current  with  the  same  temperature  rise 


ELECTRICAL  PROPERTIES   OF  CONDUCTORS    43 


as  direct  current.  In  order  to  overcome  this  it  is 
advisable  on  single  conductor  cables,  700,000  cm. 
and  larger,  for  60  cycle  circuits  and  1,250,000  cm. 
and  larger  for  25  cycle  circuits,  to  make  up  the  cable 
with  a  fibre  core  and  the  copper  stranded  around 
it.  The  weight  of  copper  in  this  type  of  cable  is 
the  same  per  foot  as  in  an  ordinary  cable,  but  owing 
to  its  annular  cross  section  the  cable  is  much  more 
efficient  in  carrying  alternating  current,  and  also 
has  a  somewhat  greater  current  carrying  capacity 
due  to  the  larger  radiating  surface. 


Size. 

Diameter 
Fiber  Core 
in  Inches. 

Number 
of  Wires 
in  Strand. 

Size  Wire 
in  Strand. 

Overall 
Diameter 
Copper 
Core. 

Ampere  Capacity. 

30°  C. 

60°  C. 

2,000,000 

7/8 

2IO 

0.099 

2.065 

1400 

1750 

1,750,000 

25/32 

210 

0.091 

.870 

1300 

1625 

1,500,000 

11/16 

162 

0.091 

.78o 

1  200 

1500 

1,250,000 

9/16 

148 

0.086 

-590 

1150 

1400 

1,000,000 

15/32 

98 

O.T02 

.280 

900 

1150 

800,000 

11/32 

51 

0.125 

.100 

775 

925 

700,000 

9/32 

51 

O.II7 

0.990 

700 

830 

(G.  E.  Co.  Bulletin.) 

4.  CARRYING  CAPACITY 

In  the  following  table  the  lower  limit  is  specified 
for  rubber-covered  wires  to  prevent  gradual  deteriora- 
tion of  the  insulation  by  the  heat  of  the  wires,  not 
from  fear  of  igniting  the  insulation. 

The  carrying  capacity  of  Nos.  16  and  18  B.  £  S. 
gauge  wire  is  given,  but  no  smaller  than  No.  14  is 
used,  except  for  fixture  work  and  flexible  cord. 


44 


ELECTRIC   POWER  CONDUCTORS 


TABLE  OF  CARRYING  CAPACITY  OF  COPPER  WIRES  AND 
CABLES— INTERIOR  WIRING 

(National  Electric  Code.) 


B.  &  S.  Gauge. 

Table  A. 
Rubber  Insulation. 
Amperes. 

TableB. 
Other  Insulations 
Amperes. 

Circular  Mils. 

18 

3 

5 

1,624 

16 

6 

8 

2,583 

14 

12 

16 

4,107 

12 

17 

23 

6,53° 

10 

24 

3  2 

10,380 

8 

33 

46 

16,510 

6 

46 

65 

26,250 

5 

54 

77 

33,i°° 

4 

65 

92 

41,740 

3 

76 

no 

52,630 

2 

90 

131 

66,370 

I 

107 

156 

63,690 

O 

l'27 

185 

105,500 

oo 

15° 

220 

133,100 

ooo 

177 

262 

167,800 

oooo 

210 

312 

211,600 

2OO 

300 

200,000 

270 

400 

300,000 

330 

500 

400,000 

39° 

590 

500,000 

450 

680 

600,000 

500 

760 

700,000 

55° 

840 

800,000 

600 

920 

900,000 

650 

I  OOO 

,000,000 

690 

1080 

,100,000 

730 

1150 

,200,000 

770 

I22O 

,300,000 

810 

1290 

,400,000 

850 

1360 

,500,000 

890 

143° 

,600,000 

93° 

1490 

,700,000 

970 

1550 

,800,000 

IOIO 

1610 

,900,000 

1050 

1670 

2,000,000 

ELECTRICAL   PROPERTIES   OF  CONDUCTORS    45 


For  insulated  aluminum  wire  the  safe  carrying 
capacity  is  84%  of  that  given  above  for  copper  wire 
with  the  same  kind  of  insulation.  (Nat.  Elec.  Code.) 

CURRENT  CARRYING   CAPACITY   OF  INSULATED   LEAD 

COVERED    COPPER    CABLES    IN    DUCTS* 

Initial  Temperature,  20°  C. 

(G.  E.  Bulletin  4591.) 


Low  TENSION  CABLE, 
SINGLE  CONDUCTOR. 

HIGH  TENSION 
CABLE,  THREE 
CONDUCTOR. 

Size  of  Cable 
in  Circular 
Mils. 

National 
Electric 
Code,  1907, 
Rubber. 

Rubber  30°  C. 
Rise. 

Var.  Cam. 
or  Paper 
60°  C.  Rise. 

Rubber  and  Var. 
Cam.  30°  C.  Rise 
Paper,  35°  C.  Rise 

Amperes. 

Amperes. 

Amperes  on  Each 
Conductor. 

2,000,000 

1050 

1400 

1750 

1,500,000 

850 

1200 

1500 

1,000,000 

650 

900 

1150 

750,000 

525 

75° 

900 

500,000 

390 

550 

660 

440 

400,000 

33° 

460 

56o 

360 

300,000 

270 

37° 

45° 

290 

250,000 

235 

230 

390 

250 

2OO,OOO 

200 

270 

310 

2IO 

150,000 

1  60 

220 

260 

175 

125,000 

140 

1  80 

210 

140 

IOO,ooo 

120 

1  60 

100 

125 

80,000 

104 

140 

I65 

110 

60,000 

82 

110 

I30 

85 

40,000 

63 

75 

90 

60 

6  B.  &  S.  solid 

46 

5° 

60 

40 

8B&S.  solid 

33 

3° 

36 

24 

10  B.  &  S.  solid 

24 

20 

24 

16 

*  The  table  gives  the  maximum  continuous  load  in  amperes  for  high  and  low 
tension  cables  with  rubber  and  varnished  cambric  or  paper  insulation,  the  ulti- 
mate rise  in  temperature  being  marked  at  the  head  of  each  column.  For  high 
tension  single  conductor,  use  figures  given  for  single  conductor  rubber. 


46  ELECTRIC   POWER  CONDUCTORS 

Experience  has  shown  that  the  maximum  tem- 
perature which  cables  should  be  permitted  to  attain 
is  50°  C.  for  rubber  and  80°  C.  for  varnished  cambric 
and  paper  insulated.  (From  G.  E.  Co.  Bulletins.) 

GENERAL  FORMULA  FOR  THE  CARRYING  CAPACITY  OF 
COPPER  WIRES  AND  CABLES: 

/  =  Current,  amperes; 

T  =  Temperature  rise,  deg.  Cent.; 


, 

K 

where 

k  is  given  by  Table     I 

A             "  "      II 

B            "  "    III 

C            "  "     IV 

D            "  "      V 

For  multiple  conductor  cables,  the  value  of  7  is 
for  one  conductor.  The  carrying  capacity  of  Alumi- 
num of  62%  conductivity  is  80%  that  of  copper. 

When  /  is  known,  and  T  is  required,  use  the  fol- 
lowing formula 

~i  +0.0042  TO 


N  —  0.0042 


ELECTRICAL   PROPERTIES   OF  CONDUCTORS    47 


where 

TO  =  initial  temperature  in  deg.  Cent. ; 

LlABCD^. 
~k0(^^)  ' 

k0  =  value  of  k  at  o  C.,  as  given  by  Table  I. 
For  Aluminum  of  62%  conductivity  £0  =  15.5. 

TABLE  I 

VALUES  OF  k 

RESISTANCE  (OHMS)  OF  A  MIL-FOOT  OF  COPPER 
Use  of  Table 

Find  the  temperature  corresponding  to  the  rise  T  by  adding  the  initial 
temperature  thereto.  Then  take  the  value  of  k  corresponding  to  that  tem- 
perature, from  the  table. 


Temperature. 

Values  of  k. 

Temperature. 

Values  of  k. 

°C 

op 

98% 
Conduc- 

99% 
Conduc- 

°C 

0  F. 

98% 
Conduc- 

99% 
Conduc- 

tivity. 

tivity. 

tivity. 

tivity. 

0 

32 

9-79 

9.69 

55 

13* 

12.0 

11.9 

5 

4i 

10.  0 

9-9° 

60 

140 

12.2 

12.  I 

10 

50 

10.2 

10.  I 

65 

149 

12.4 

12.3 

15-5 

60 

IO.4 

10.3 

70 

158 

12.7 

12-5 

20 

68 

10.6 

10.5 

75 

157 

12.9 

12.7 

24 

75-2 

10.8 

10.7 

80 

176 

13-1 

I2.9 

30 

86 

II.  O 

10.9 

85 

185 

13-3 

I3-I 

35 

95 

II.  2 

n.  i 

90 

194 

13.5 

13-4 

40 

104 

ii.  4 

n-3 

95 

203 

13.7 

13-6 

45 

U3 

ii.  6 

"-5 

IOO 

212 

13-9 

13-7 

50 

122 

ii.  8 

1.1.7 

on  Matthiessen's  Standard  and  the  A.I.E.E.  temperature  coefficient. 


ELECTRIC   POWER  CONDUCTORS 


TABLE  II 

VALUES  OF  A 


where  d=  diameter  of  a  solid  wire  of  the  size  given,  inches 


Size  of  Conductor. 

A. 

Size  of  Conductor. 

A. 

Millions  of  C.M. 

No.  B.  &  S. 

2 

i-9 
1.8 

10.32 
9-93 
9-54 

oooo 
ooo 

00 

1.91 
1.61 
i-35 

-7 
.6 

-5 

9.14 
8.74 
8.32 

o 

I 

2 

1.14 

°-955 
0.802 

-4 
-3 

.2 

7-9° 
7.46 

7-03 

3 

4 
5 

0.675 
0.566 
0.476 

I.I 
1.0 

0.9 

6-59 
6-15 
5-67 

6 

7 
8 

0.400 

o-337 
0.282 

0.8 

5-i9 

9 

0.237 

o-75 

4-95 

10 

0.200 

o-7 

4-7° 

12 

0.147 

0.6 

o-S 
0.4 

4.18 

3-65 
3-o8 

14 

16 
18 

0.0995 

0.0703 
0.0496 

o-35 
°-3 

2-79 
2-49 

20 

22 

0.0351 

0.0248 

0.25 

2.17 

ELECTRICAL   PROPERTIES   OF  CONDUCTORS   49 
TABLE  III 

VALUE  OF  B 


W=  watts  dissipated  per  sq.in.  of  single  conductor  cable  per  deg.  Cent. 
Temperature  rise. 


Where  Installed. 

Type  of  Cable. 

Bare. 

Rubber  Covered. 

Paper  or  Cloth 
and  Lead. 

Solid. 

Stranded. 

Solid. 

Stranded. 

Solid. 

Stranded. 

Open  air  ... 

1  60 
130 

175 
143 

105 
94 
140 

89 
78 
75 

no 

no 

IOO 

150 

93 
82 

79 
US 

105 
89 

86 

75 
72 

IOO 

no 
93 

90 
79 
75 

105 

Still  air  

Wooden  moulding.. 
3J"  tile  duct; 
No.  oooo  B.  &  S.  . 
|M.  . 

iM 

Under  water,  leaded 
and  armored  

The  values  given  in  the  above  table  are  averages  based  on  experimental  data 
from  various  sources ;  the  maximum  variation  from  the  average  in  the  values  thus 
found  was  about  5%. 


TABLE  IV 

VALUE  OF  C 

(Standard  Underground  Cable  Co.  Handbook.) 


Type  of  Cable. 

C. 

Single  conductor  

i 

Two  conductor,  flat  or  round  

o  87 

Two  conductor,  concentric.  .  . 

O   7c) 

Three  conductor,  triplex  

O  7? 

Three  conductor,  concentric 

o  60 

50 


ELECTRIC    POWER  CONDUCTORS 


TABLE  V 

VALUES  OF  D 


Number  of  Simi- 
larly Loaded  Cables 
in  Group  of 
Ducts. 

D. 

I 

i  .0 

2 

3 

0.92 
0.86 

4 

o-79 

5 
6 

7 
8 

o-75 
0.70 
0.66 
0.63 

9 

10 

°-59 
0.56 

12 

0.& 

The  thickness  of  insulation  probably  has  a  considerable  effect  upon  the  radiation, 
but  experimental  data  on  this  point  are  not  available.  The  above  table  is  based 
principally  upon  tests  of  low  voltage  cables. 


Carrying  Capacity  of   Wires  of  Various   Metals.      The 

carrying  capacity  or  current  causing  a  given  tem- 
perature rise  is  inversely  proportional  to  the  square 
root  of  the  specific  resistance  of  the  metal,  and 
directly  proportional  to  the  square  root  of  the  heat 
radiation  per  unit  area.  Assuming  the  latter  to  be 
the  same  for  all  wires,  the  relative  carrying  capaci- 
ties of  wires  of  different  metals,  referred  to  Matthies- 
sen's  annealed  copper  as  unity  are  given  in  the 
following  table; 


ELECTRICAL   PROPERTIES   OF  CONDUCTORS    51 


Metal. 

Relative  Carry- 
ing Capacity. 

Silver,  annealed  

1  .04 

Copper   annealed 

o  oo  to  I   01 

Copper,  annealed,  100%  cond... 
Copper  or  silver,  hard  drawn.  .  .  . 
Gold   hard  drawn.  .  . 

I 
0.98  to  i.o 
o  87 

Aluminum,  annealed  

0.74 

Aluminum  wire,  62*%  cond 

O   70 

Zinc   pressed.  .        

o.  <3 

Phosphor  bronze 

O    4  < 

Platinum   annealed. 

o  42 

Iron,  annealed  

0.40 

Nickel   annealed 

o  36 

Tin,  pressed  

O.  "?  ^ 

Lead   pressed 

O    2O 

German  silver,     from  

o  28 

to 

O    2  T. 

Platinoid  

O    22 

Antimony  pressed 

O    21 

Mancanin             .  - 

O    IO 

Krupp  metal 

O    14 

^tercury 

O    I  3 

Bismuth.  Dressed.  . 

0.  12 

Knowing  Heating  with  One  Current,  to  Find  Heating 
with  Another  Current.  The  chart  (Fig.  6)  is  used  as 
follows : 

Suppose  a  switch  or  cable  has  a  rise  of  20°  C.  with 
200  amperes,  what  will  the  rise  be  with  300  amperes? 
Referring  to  the  curve,  the  vertical  line  200  is  followed 
upward  until  it  intersects  the  diagonal  which  starts 
at  20°.  This  diagonal  is  followed  upward  until  it 
intersects  a  vertical  line  at  300  amperes.  The  hori- 
zontal line  intersecting  the  vertical  line  at  this  point 
gives  the  rise  in  degrees,  namely,  45. 


52 


ELECTRIC   POWER  CONDUCTORS 


As  noted  on  the  diagram  the  current  scale  is  cor- 
rect for  amperes,   milli -amperes,   or  any  other  unit, 


100 

90 


70 


.i60 

5 

.«  80 


40 


30 


20 


15 


10 


////  I//// // //////// I/I 


LLL 


ILL 


LL 


LULL 


J/ILIULULUL 


7      A 


'LL 


'JL    I 


100       150     200        300    400   500  600  700  800  900  1000 
Current  in  any  Unit. 
FIG.  6. 

and  the  temperature  scale  is  correct  for  either  Centi- 
grade or  Fahrenheit.  (Based  on  article  by  C.  C. 
Badeau,  Elec.  World,  Jan.  n,  1908.) 


ELECTRICAL   PROPERTIES    OF  CONDUCTORS    53 


INTERMITTENT  CARRYING  CAPACITY 
Let  P  =  time  of  full  period  (minutes)  assuming  the 

current  periodically  on  and  off; 
a  =  portion  of  f till  period  (minutes)  that  current 

is  on; 

T  =  time  (minutes)   in  which  temperature  rise 
becomes  0.633  times  maximum  tempera- 
ture rise.     This  depends  on  size  and  type 
of  cable  and  is  given  in  the  following  table : 
C  =  maximum  permissible  constant  current; 
pC  =  maximum  permissible  intermittent  current. 
To  find  pC: 

Find  T  for  size  of  cable  under  consideration. 

Thence   calculate  —   and   —   and   from   the    table 
find  the  corresponding  value  of  p. 

VALUES  OF  T 
CABLE  INSULATED  FOR  700  VOLTS 


Sq.Mm. 

Value  of  T. 

Single  Cond. 

Triplex. 

50 

14 

21 

100 

21 

32 

J50 

28 

42 

200 

32 

50 

300 

38 

63 

400 

41 

70 

500 

42 

600 

44 

700 

46 

800 

48 

yoo 

49 

IOOO 

50 

54  ELECTRIC   POWER  CONDUCTORS 

VALUES  OF  p 


a 

a 

P 

T 

O.  I. 

0.15. 

0.2. 

0.3. 

0.4. 

0.5- 

0.6. 

0.7. 

0.8. 

0.9 

o.o 

3-15 

2.65 

2.25 

.8 

-55 

-45 

-3 

1.2 

I.I 

-05 

0    I 

2.  «:< 

2.T.Z 

2.2 

.7 

.  c; 

•  4 

.25 

.Ot? 

O    2 

2    2 

2.OZ 

I    n 

.6 

-4s 

?c; 

2C 

oc 

o  3 

-0 

.85 

I  -7 

-  ^ 

.4 

.  7 

ex 

o  4 

.7 

.7 

1.6 

.  < 

.7C 

.  T. 

-O<? 

o  ? 

6 

CJC 

I    cir 

4^ 

•2 

? 

2 

I     If 

oc 

i.o 

-25 

•25 

1.25 

-25 

.2 

.2 

•  IS 

I.I 

1.05 

-°5 

2.0 

-05 

-05 

1.05 

-05 

-05 

-05 

-05 

1.05 

1.05 

-05 

00 

I.O 

I.O 

I.O 

.0 

.0 

.0 

.0 

I.O 

I.O 

.0 

THE   SHORT-PERIOD   CARRYING  CAPACITY  OF  CABLES* 

The  formula  should  not  be  used  without  under- 
standing the  assumptions  made  in  deriving  it;  for 
although  they  are  quite  reasonable  under  ordinary 
conditions,  they  do  not  necessarily  hold  under  certain 
extreme  conditions.  These  assumptions  are  as  fol- 
lows: 

(1)  That  the  heat  dissipated  by  the  cable  is  directly 
proportional  to  the  temperature  rise. 

(2)  That  the  specific  heat  of  the  conductor  and 
insulation  does  not  vary  greatly  over  the  tempera- 
ture  range   considered,    an   average   value   being   as- 
sumed. 

(3)  That  the  caole  insulation  is  raised  to  the  same 
temperature   as   the   conductor.     This   asstimption  is 
approximately  correct  for   thin   insulation   on   large 

*  Electrical  World,  Dec.  12,  1908. 


•   * 
ELECTRICAL  PROPERTIES  OF  CONDUCTORS    55 

cables;  the  assumption  is  not  true  for  cables  smaller 
than  No.  oo  B.  &  S.,  or  for  cables  insulated  for  over 
1000  volts.  This  restriction  is  of  little  moment, 
however,  as  the  important  use  of  the  formula  is  in 
connection  with  large  power  cables,  a  knowledge  of 
the  carrying  capacity  of  which  may  lead  to  consider- 
able economy  of  copper. 

The  following  formula  gives  the  time  (t  =  minutes) 
during  which  a  cable  will  carry  /  amperes  with  a 
temperature  rise  of  D  deg.  Fahr.  : 


P,  A,  K,  and  G  are  constants  of  the  cable  and  are 
denned  as  follows  : 

P  =  [(specific  heat  of  conductor  X  weight  in  pounds 
per  foot)  +  (specific  heat  of  insulation  X  weight 
in  pounds  per  foot)]; 

A  =  cross-sectional  area  of  cable  in  circ.  mils  ; 

K  =  average  of  the  reciprocals  of  the  ohms  per  mil- 
foot  over  the  range  of  temperature  considered. 
For  practical  purposes  AK  is  the  reciprocal  of 
the  resistance  per  foot  of  the  cable  at  the 
temperature  midway  between  the  initial  and 
final  temperatures  assumed; 

F 
£  =  p  where  F  is  the  final  temperature  rise  which 

would  occur  with  I  amperes  applied  steadily. 


56  ELECTRIC   POWER  CONDUCTORS 

It  is  a  constant  for  every  cable  under  given 
conditions  of  thermal  exposure,  and  may  be 
obtained  from  any  pair  of  values  of  F  and  /. 

Z  is  a  function  of  7^-,  which  in  turn  equals  —  and 
GI2  F 

may  be  taken  from  Table  I  or  calculated  by 
the  formula, 

D 


the  logarithm  being  to  the  base  10. 

The  product,  40.5  PAKG,  which  is  a  constant  for 
a  given  cable  under  ^iven  conditions,  is  the  time  in 
minutes  required  to  raise  the  temperature  of  the 
cable  to  90%  of  its  final  temperature  rise. 


ELECTRICAL  PROPERTIES  OF  CONDUCTORS   57 


TABLE  I 

VALUES  OF  Z 


D      D 
GI*     F 

Z 

D       D 

GT^T 

Z 

D      D 

GT*=T 

Z. 

0.005 

0.00218 

O.OI 

0.00436 

0.31 

0.161 

0.61 

0.409 

O.O2 

0.00877 

0.32 

0.167 

0.62 

0.420 

O.O3 

0.0132 

0-33 

0.174 

0.63 

0.432 

O.O4 

0.0177 

0-34 

0.180 

0.64 

0-444 

O.O5 

0.0223 

0-35 

0.187 

0.65 

0.456 

O.O6 

0.0269 

0.36 

0.194 

0.66 

0.469 

0.07 

0.0315 

0-37 

O.2OI 

0.67 

0.481 

<xo8 

0.0362 

0.38 

0.208 

0.68 

o-495 

0.09 

0.0410 

o-39 

0.215 

0.69 

0.509 

O.IO 

0.0458 

0.40 

O.222 

0.70 

0-523 

O.II 

0.0506 

0.41 

0.229 

0.71 

0.538 

O.I2 

0.0555 

0.42 

0.237 

0.72 

0-553 

0.13 

0.0605 

o.43 

0.244 

o-73 

0.569 

0.14 

0.0655 

0.44 

0.252 

0.74 

0.585 

0-15 

0.0706 

0-45 

0.26O 

0-75 

0.602 

0.16 

0.0757 

0.46 

0.268 

0.76 

0.620 

0.17 

0.0809 

o.47 

0.276 

0.77 

0.638 

0.18 

0.0861 

0.48 

0.284 

0.78 

0.658 

0.19 

0.0915 

0.49 

O.292 

0.79 

0.678 

0.20 

0.0969 

0.50 

0.301 

0.80 

0.699 

O.2I 

O.I02 

0.51 

0.310 

0.81 

0.721 

0.22 

0.108 

0.52 

0.319 

0.82 

o-745 

0.23 

O.II3 

o-53 

0.328 

0.83 

0.770 

O.24 

O.II9 

0-54 

o-337 

0.84 

o-795 

0.25 

0.125 

0-55 

o-347 

0.85 

0.824 

0.26 

O.I3I 

0.56 

o-357 

0.86 

0.854 

0.27 

0.137 

o.57 

0.367 

0.87 

0.886 

0.28 

O.I42 

0.58 

0.377 

0.88 

0.921 

0.29 

0-149 

0-59 

0.387 

0.89 

o-959 

0.30 

0-155 

0.60 

0.398 

0.90 

I.OOO 

58 


ELECTRIC   POWER  CONDUCTORS 


TABLE  II 

VALUES  OF  P  FOR  BARE  COPPER  CABLES 

Specific  heat  =  0.093. 


Size 

No.  of  Strands. 

P. 

2    million  C.M. 
Ij 

127 
91 

0-558 
0.425 

i 
1 

i 

91 
61 

61 

61 

o-354 
0.284 

O.2I2 
O.I42 

oooo  B.  &  S. 

37 

0.0709 

o  .  0600 

ooo  B.  &  S. 

19 

0.0476 

For  aluminum  of  the  same  resistance,  increase  P  by  1 1  per  cent. 

TABLE  III 

RECIPROCALS  OF  OHMS  PER  MIL-FOOT 


Deg.  P. 

Reciprocal  of  Ohms 
per  Mil.-Foot. 

Deg.  F. 

Reciprocal  of  Ohms 
per  Mil.  Foot. 

50 

0.0980 

IOO 

0.0883 

55 

0.0970 

I05 

0.0874 

60 

0.0960 

no 

0.0866 

65 

0.0950 

H5 

0.0858 

70 

0.0940 

1  20 

0.0850 

75 

0.0930 

125 

0.0842 

80 

o  0920 

130 

0.0833 

85 

0.0910 

135 

0.0826 

90 

o  .  0900 

140 

0.0818 

95 

0.0892 

U5 

0.0811 

TOO 

0.0883 

150 

0.0804 

The  above  table  is  based  on  98  %  conductivity. 


CHAPTER  III 
INSULATION  AND   INSULATED  CONDUCTORS 

i.  INSULATION 

THE  principal  materials  used  for  insulating  power 
cables  are: 

(1)  Paper  saturated  with  oil. 

(2)  Varnished    muslin,    variously    known    as    var- 
nished cambric  or  varnished  cloth. 

(3)  Compounds  containing  rubber. 

The  first  two,  being  made  of  staple  commercial 
materials,  are  generally  reliable,  but  compounds  con- 
taining rubber  vary  from  the  cheap  material  used 
for  insulating  "  code  wire  "  to  the  high-grade  com- 
pound required  by  the  U.  S.  Navy. 

NECESSITY  OF  UNIFORM  STRUCTURE 

If  two  conducting  plates  are  arranged  at  such  a 
distance  apart  that  the  air  is  just  able  to  withstand 
for  an  indefinite  time,  say,  10,000  volts  maintained 
by  a  transformer,  and  then  a  strip  of  glass  is  intro- 
duced between  them,  the  insulation  will  break  down, 

59 


60  ELECTRIC  POWER  CONDUCTORS 

although  the  glass  has  greater  dielectric  strength 
than  air.  The  explanation  is  quite  simple:  the  fall 
of  volts  per  centimeter  in  the  air  before  the  glass  is 
inserted  is  the  highest  the  air  can  withstand;  as 
glass  has  a  higher  specific  inductive  capacity  the 
potential  gradient  in  the  glass  is  less  steep  than  in 
the  air,  and  the  consequent  increased  steepness  in 
the  air  due  to  the  insertion  of  the  glass,  causes  the 
air  to  break  down.  This  experiment  shows  the 
necessity  of  having  the  insulation  free  from  air 
spaces  or  weak  spots,  and  in  the  case  of  high  tension 
cables,  of  having  no  air  spaces  between  insulation 
and  sheath;  it  also  explains  why  an  insulated  cable 
without  a  sheath  should  not  be  supported  directly 
on  metal  brackets.  However,  by  adapting  the  specific 
inductive  capacity  of  the  insulations  to  the  potential 
gradient,  an  increased  total  dielectric  strength  may 
be  obtained  as  in  "  graded  "  cables;  that  is,  those 
in  which  the  small  area  in  contact  with  the  conductor 
is  made  of  greater  specific  inductive  capacity  than  the 
peripheral  areas,  in  order  to  decrease  the  potential 
gradient  in  the  insulation  adjacent  to  the  conductor. 

RUBBER  INSULATION 

Rubber  insulation,  so-called,  is  a  compound  of 
various  substances  in  which  rubber  seldom  pre- 
dominates. It  is  therefore  not  surprising  to  find 
the  properties  of  rubber  compounds  varying  between 
very  wide  limits  according  to  the  nature  of  the 


INSULATION  AND  INSULATED  CONDUCTORS    61 

substances  of  which  they  are  composed,  and  accord- 
ing to  the  process  of  compounding. 

The  qualities  which  a  rubber  compound  should 
possess,  in  order  to  fulfil  all  requirements  as  cable 
insulation,  are  as  follows: 

(1)  High  dielectric  strength. 

(2)  High  mechanical  strength. 

(3)  Fair  elasticity. 

(4)  Fair  specific  resistance. 

(5)  Permanence  or  long  life. 

The  first  four  qualities  are  not  difficult  to  obtain. 
and  it  is  easy  to  test  a  compound  for  their  presence. 
The  fifth  quality,  permanence,  depends  upon  two 
conditions.  The  first  of  these  is  chemical  equilibrium, 
i.e.,  the  rubber  and  substances  associated  with  it 
must  have  no  affinity  forgone  another,  for  the  con- 
ductor, for  air  or  for  moisture.  The  second  condition 
is  that  the  compound  shall  contain  no  substance 
tending  to  change  its  physical  state,  as  for  example, 
a  volatile,  photo-sensitive  or  crystallizable  substance. 

Within  wide  limits  compounds  of  various  com- 
positions can  be  made  balanced,  and  therefore 
permanent,  provided  that  conditions  inconsistent 
with  the  condition  of  balance  are  not  specified. 
There  are  no  known  tests  which  will  infallibly  dis- 
tinguish between  a  balanced  and  an  unbalanced 
compound.  A  short  discussion  of  the  tests  and 
restrictions  which  have  been  suggested  for  this 
purpose  is  given  below. 


OF   THE 

UNIVERSITY 


62  ELECTRIC  POWER  CONDUCTORS 

RUBBER  GUM 

Rubber  is  a  gum  extracted  from  a  tree  which 
grows  in  the  tropical  countries  of  Africa  and  South 
America.  The  quality  of  this  gum  varies  in  many 
ways,  but  the  characteristic  which  most  affects  its 
commercial  value  is  the  amount  of  resinous  extract 
which  it  contains.  The  amount  of  extract  is  usually 
estimated  by  digesting  the  gum  in  acetone  for  sev- 
eral hours,  and  thereby  dissolving  out  the  extract. 
The  proportion  of  acetone  extract  in  different  grades 
of  gum  varies  from  less  than  i  per  cent  to  over  20 
per  cent,  the  grades  having  the  smaller  proportion 
of  extract  being  generally  from  South  America. 

The  best  grade  of  South  American  rubber  is  known 
as  fine  Para,  and  is  the  most  desirable  kind  to  use 
in  insulating  compounds.  While  it  is  usual  to 
specify  that  compounds  shall  contain  only  the  finest 
dry  Para  rubber,  there  is  no  practical  way  to  ascer- 
tain whether  the  rubber  did  actually  come  from 
Para.  Furthermore,  it  is  of  no  practical  import 
whence  the  rubber  is  from,  provided  that  the  per- 
centage of  extract  does  not  exceed,  say,  3  per  cent. 
A  greater  percentage  of  extract  indicates  a  cheap 
grade  of  rubber,  which  it  is  difficult  to  manufacture 
into  a  balanced  compound. 


INSULATION  AND  INSULATED  CONDUCTORS    63 
VULCANIZATION 

Rubber  gum,  in  its  native  state,  is  of  little  use 
for  insulating  purposes,  owing  to  its  property  of 
absorbing  water  and  oxidizing.  When  mixed  with 
sulphur  and  heated  to  a  temperature  of  from  248° 
to  302°  Fahr.,  a  combination  takes  place  which 
renders  the  rubber  more  stable  and  at  the  same 
time  increases  its  mechanical  and  electrical  strength. 
This  process  is  known  as  vulcanization. 

COMPOUNDING 

It  has  been  found  by*  experience  that  60  to  70 
per  cent  of  adulterant  may  be  added  to  rubber  gum 
without  destroying  its  useful  qualities  after  vul- 
canization. Above  this  percentage,  the  qualities  of 
the  rubber  cease  to  predominate,  and  the  compound 
partakes  markedly  of  the  characteristics  of  the 
adulterant.  It  is  for  this  reason  that  30  per  cent 
pure  rubber  is  generally  adopted  as  the  standard 
proportion,  and  that  40  per  cent  pure  rubber  is 
required  for  shipboard  work  in  the  navy,  the  larger 
proportion  being  adopted  as  a  special  precaution  on 
account  of  the  necessity  of  absolute  reliability. 

TENSILE  STRENGTH 

A  good  30%  Para  compound,  properly  vulcanized, 
should  show  a  tensile  strength  of  at  least  800  pounds 
per  square  inch.  This  figure  is  agreed  to  by  prac- 


64  ELECTRIC  POWER  CONDUCTORS 

tically  every  manufacturer  of  rubber  compound  in 
the  United  States,  but  the  proportion  of  compounds 
which  actually  show  this  tensile  strength  is  small. 

A  sample  should  be  cut  so  that  the  ends  gripped 
shall  be  considerably  larger  than  the  center,  \vhere 
the  break  should  occur.  The  sample  should  be  bent 
slightly,  in  every  direction,  before  testing,  in  order 
to  magnify  and  reveal  any  surface  incisions  which 
might  reduce  the  total  cross-section. 

SET  AFTER  STRETCHING 

When  stretched  three  times  its  original  length,  a 
sample  should  show  a  set  not  greater  than  i8|% 
after  a  stated  time  has  elapsed.  Although  the  time 
is  a  matter  of  controversy,  this  percentage  set  is 
agreed  to  by  all  the  leading  manufacturers. 

Nevertheless,  it  is  well  known  that  certain  excel- 
lent compounds  entirely  fail  to  meet  the  regular 
stretch  tests.  It  is,  perhaps,  better  to  lose  the  use 
of  this  class  of  compounds  and  take  advantage  of  the 
selective  action  of  the  stretch  test;  and  if  this  is 
done  it  should  be  specified  that  the  test  may  be 
performed  by  the  purchaser  at  any  temperature 
between  50°  and  100°  Fahr.  It  should  also  be  speci- 
fied that  the  sample  tested  shall  not  have  been  sub- 
mitted to  any  previous  stretching,  because  a  sample 
with  a  permanent  set  will  not  show  much  additional 
set  when  further  stretched.  Stretching  should  be 
steadv  and  release  instantaneous. 


•  * 
INSULATION  AND  INSULATED  CONDUCTORS    65 

SPECIFIC  RESISTANCE 

The  specific  resistance  of  insulation  sold  as  30% 
Para  compound  varies  between  the  enormously  wide 
limits  of  150  millions  of  megohms  per  inch  cube 
and  4000  millions  of  megohms  per  inch  cube. 

From  the  standpoint  of  leakage  a  mere  fraction 
of  the  smaller  value  would  be  sufficient.  It  is,  there- 
fore, only  as  a  test  of  quality  that  high  megohms 
may  be  demanded,  and  the  value  of  such  test  is  open 
to  doubt. 

A  minimum  of  750  millions  of  megohms  per  inch 
cube  is  conservative,  and  there  is  certainly  nothing 
to  be  gained  by  specifying  over  1200  millions  of 
megohms  per  inch  cube. 

Much  more  important  is  the  permanence  of  the 
insulation  resistance.  A  good  compound  should  show 
little  decrease  of  insulation  resistance  after  100  hours 
of  test  with  current  applied  continuously. 

TEMPERATURE  COEFFICIENT  OF  RESISTANCE 

The  rate  of  change  of  resistance  with  regard  to 
temperature  should  not  exceed  2.6%  per  degree  Fahr. 
This  is  in  agreement  with  the  tables  used  by  the 
most  reputable  manufacturers.  The  object  of  speci- 
fying this  quantity  is  twofold:  First,  to  prevent  the 
manufacturer  using  any  temperature  correction  factor 
which  will  give  a  figure  which  complies  with  the 
specifications;  second,  as  a  measure  of  quality  of 


66 


ELECTRIC  POWER  CONDUCTORS 


the  compound  as  pointed  out  by  H.  G.  Stott,  Proc. 
Am.  Inst.  Elec.  Eng.,  1906. 

The  author's  experience  confirms  Mr.  Stott's  opinion 
of  the  value  of  this  test. 


"  HYSTERESIS  TEST  » 


If  extensions  and  contractions  are  plotted  on  a 
base  of  load,  a  "  hysteresis  "  loop  is  obtained,  as 
shown  in  Fig.  7.  The  area  of  this  loop  should 


Stress,  Ibs.  per  sq.  in.  of  Original  Area. 

FIG.  7. 

generally   be    small    in    good    compound;    there    are, 
however,  exceptions  to  this  rule. 

SULPHUR 

Sulphur    in    rubber    compound    may    be    in    three 
conditions : 

(1)  Free; 

(2)  Combined  with  rubber; 

(3)  In  barium  sulphate,  etc. 


INSULATION  AND  INSULATED  CONDUCTORS    67 


Poor  quality  rubber  requires  a'  great  deal  of  sulphur 
to  vulcanize  it,  and  is,  therefore,  often  revealed  by 
the  large  amount  of  combined  sulphur. 

Excess  of  free  sulphur,  say  over  1%,  usually  indi- 
cates an  unstable  compound,  as  the  sulphur  is  liable 
to  combine  with  the  copper  or  tin  coating  over  the 
copper. 

PERCENTAGE  OF  RESINOUS  MATTER 


Brand  of  Rubber. 

Resin  in 
Washed  Rub- 
bei,  Per  Cent. 

Resin  in 
Vulcanized  Rub- 
ber, Per  Cent. 

Para  fine 

I    2 

4  O4. 

Ceara                                                    

2    I 

^    12 

Upper  Congo  

7.7 

7.60 

Lagos 

A    r 

717 

Sierra  Leone  

6.1 

0-Q7 

Borneo 

TO    7. 

14   44 

C.  O.  Weber,  "Chemistry  of  India  Rubber." 
EFFECT  OF  TEMPERATURE  ON  RUBBER 

Rubber  insulation  begins  to  deteriorate  at  ordinary 
air  temperatures;  the  deterioration  is  rapidly  acceler- 
ated when  exposed  to  temperatures  in  excess  of  50°  C. 
The  following  are  the  effects  noted. 

(1)  Loss  of  Strength  or  Cohesion.     Rubber  with  a 
low  coefficient  of  vulcanization  is  liable  to  develop 
this  defect,  particularly  if  the  time  for  vulcanization 
has  been  short. 

(2)  Hardening  with  Brittleness.     Rubber  may  con- 
tain   white    substitutes    (chlorosulphides) ,    but    more 


ELECTRIC  POWER  CONDUCTORS 

mmonly  is  due  to  the  presence  of  a  considerable 
amount  of  free  sulphur. 

(3)  Stickiness  and  Darkening  in  Color.  Rubber 
containing  mineral  oils,  large  quantities  of  recovered 
rubber,  or  large  proportions  of  sulphide  substitutes. 


Temperature 
Deg.  Cent 

pO-lOO 

MS 

150-160 
170-190 

240 

255 
340* 


Change  in  State  of  Para  Rubber  with  Temperature 

Slightly  sticky. 

Sticky,  but  slightly  elastic. 

Surface  melts  and  rubber  darkens. 

Gradually  melts. 

Can  be  mixed  up  and  thermometer  easily 

pushed  into  the  mass. 
Appearance  of  decomposition  and  boiling. 
Gas  evolved,  which  burns  with  a  luminous 

flame. 


The  liquid  obtained  on  heating  becomes  viscid  on 
cooling,  but  it  does  not  again  solidify. 

TENACITY  AND  TEMPERATURE 


Temperature  in 
Deg.  F. 

Loss  of  Tenacity, 
Per  Cent. 

68 

2 

138 

5 

248 

10 

328 

15 

418 

20 

438 

22 

488 

25 

A.  Schwartz,  Journal  Inst.  E.  E.,  1907. 


•    * 
INSULATION   AND  INSULATED  CONDUCTORS    69 

RUBBER  INSULATION  UNDER  WATER 

Rubber  insulation  will  last  indefinitely  under  fresh 
or  salt  water  if  the  compound  is  balanced  and  if  the 
water  is  not  contaminated  with  sewage,  etc.  Where 
the  insulation  is  intended  for  this  service,  the  manu- 
facturer should  be  so  advised. 

EFFECT  OF  OVER-MASTICATION  OF  RUBBER 

Rubber  overworked  in  the  masticator  oxidizes 
very  rapidly,  yielding  a  much  greater  amount  of 
extract  than  before  mastication.  (C.  O.  Weber, 
Journal  of  Society  of  Chemical  Industry,  1903,  p.  875 
and  p.  103.) 

EFFECT  OF  LIGHT  ON  RUBBER 

The  action  of  light  on  rubber,  whether  vulcanized 
or  unvulcanized,  is  an  oxidizing  action,  but  the 
oxidation  is  faster  the  lower  the  degree  of  vulcani- 
zation. (C.  O.  Weber,  Journal  of  Society  of  Chemical 
Industry,  1903,  p.  875.) 

The  significance  of  this  statement  has  been  over- 
looked by  the  majority  of  manufacturers  and  users 
of  rubber.  If  a  number  of  samples  of  rubber  insula- 
tion of  different  makes  are  subjected  for  a  long 
period  to  the  action  of  light,  those  compounds 
which  are  black  will  almost  invariably  remain 
unchanged,  while  those  which  are  white  or  of  light 
shade,  will  become  stiff  and  brittle.  This  fact  has 


70  ELECTRIC  POWER  CONDUCTORS 

been  made  use  of  by  certain  manufacturers  of  black 
compounds,  who  claim  that  their  product  has  a 
longer  life  than  others,  because  when  subjected 
to  the  open  air  "  weathering  test  "  it  outlasts  nearly 
all  others.  This  claim  is  unjustifiable  because  the 
test  is  really  a  photo-chemical  one  and  has  nothing 
to  do  with  weathering.  If  protected  from  light, 
the  white  compounds  last  as  well  as  the  black  ones, 
and  are  therefore  just  as  good  if  used  under  black 
braiding  or  lead  sheathing. 

The  explanation  of  these  facts  is  that  rubber  is 
normally  translucent  and  unless  rendered  quite 
opaque  by  the  presence  of  black  matter  is  affected 
photo-chemically  throughout  its  mass.  Black  com- 
pounds, on  the  other  hand,  are  only  affected  super- 
ficially by  light,  becoming  coated  with  a  powdery, 
white  film,  which  is  readily  brushed  off. 

DETERIORATION  OF  CONGO  RUBBER 

The  deterioration  of  Congo  rubber  is  due  to 
the  presence  of  albuminous  substances  primarily. 
Coagulated  albumin  is  not  removed  by  washing, 
causing  finished  goods  to  be  more  or  less  brittle, 
according  to  the  amount  of  albumin  present.  (C.  O. 
Weber,  Journal  of  Society  of  Chemical  Industry,  1902, 
p.  712.) 


* 

INSULATION  AND  INSULATED  CONDUCTORS    71 

EXCESS  OF  LITHARGE 

Certain  varieties  of  rubber  do  not  become  prop- 
erly vulcanized  when  treated  with  sulphur  only, 
but  do  so  readily  if  a  considerable  proportion  of 
litharge  is  present  during  the  process.  The  effect 
of  litharge,  however,  is  to  make  the  rubber  brittle. 
(C.  O.  Weber,  journal  of  Society  of  Chemical  Industry, 
1903,  p.  103.) 

AVERAGE  DIELECTRIC  STRENGTH  OF  RUBBER  INSULATION 

128  kilo  volts  per  in.,  conservative  testing  stress. 

56  kilo  volts  per  in.,  conservative  working  stress. 

400  kilo  volts  per  in.,  breakdown  stress  (approx.). 

PAPER  INSULATION 

Paper  ribbon  is  wound  spirally  around  the  con- 
ductor in  numerous  layers,  until  the  desired  thick- 
ness is  obtained.  The  cable  is  then  immersed 
in  a  bath  of  oily  insulating  compound,  until  satu- 
rated. The  whole  is  then  enclosed  in  a  lead  sheath, 
which  not  only  serves  to  retain  the  compound,  but 
also  to  exclude  moisture. 

This  type  of  cable  is  cheaper  than  varnished 
cambric  or  good  quality  rubber,  and  is  almost 
universally  used  for  voltages  from  5000  up.  It  is 
also  very  largely  used  for  lower  voltages. 

Owing  to  the  hygroscopic  qualities  of  paper  insu- 
lation, it  should  not  be  used  where  the  cable  is 
exposed  to  the  direct  action  of  water,  as,  for  example, 


72 


ELECTRIC  POWER  CONDUCTORS 


in  submarine  work,  or  in  badly  drained  splicing 
chambers.  For  this  service,  rubber  or  varnished 
cambric  insulation  is  to  be  preferred,  as,  in  the 
event  of  a  burn-out,  the  insulation  will  not  be 
spoiled,  except  at  the  actual  point  of  trouble. 

Dr.  Jona  (Int.  Elec.  Congress,  1904),  says  that 
paper  subjected  to  dielectric  strain  for  an  hour, 
with  progressively  increasing  voltage,  will  stand 
from  eight  to  ten  kilovolts  per  millimeter.  These 
numbers  represent  good  commercial  averages,  but 
it  is  not  unusual  to  find  paper  with  20  or  30  per 
cent  greater  dielectric  strength. 

FACTORS  FOR  CORRECTION  OF  INSULATION  RESISTANCE 

TO  15.5°  C. 


Temperature, 
Deg.  C. 

Factor  for  High- 
Grade  Paper. 

3° 

5.38 

2Q 

5-20 

28 

4.82 

27 

4-45 

26 

4.09 

25 

3-7i 

24 

3-32 

23 

2-Q7 

22 

2.61 

21 

2.24 

20 

2.  CO 

»9 

I.78 

18 

i-57 

*7 

1-36 

16 

1.14 

1  5.  5  (60°  F.) 

I.  00 

i5 

0.92 

14 

0.78 

INSULATION  AND  INSULATED  CONDUCTORS    73 

The  resistance  at  15.5°  C.  is  found  by  multiplying 
the  observed  resistance  by  the  factor  correspond- 
ing to  the  temperature  at  which  the  resistance  is 
measured. 

VARIATION  OF  INSULATION  RESISTANCE  WITH  TIME  OF 
ELECTRIFICATION  (PAPER  INSULATION) 


Relative  Insulation 

Time  of  Electrifica- 
tion, Minutes. 

Resistance,  Referred 
to  Value  after  One 
Minute  Electrifica- 

tion. 

0 

oj 

0.824 

I 

.00 

ii 

.09 

2 

.16 

2* 

.21 

3 

.24 

3* 

.28 

4 

-31 

4* 

5 

i-35 

This  test  represents  average  results,  but  must  not  be  taken  as  correct  for  any 
particular  cable. 


VARNISHED  CAMBRIC 

Prepared  cotton  fabric  is  coated  on  both  sides 
with  multiple  films  of  insulating  varnish.  The  coated 
cloth  is  cut  into  strips  and  wound  spirally  on  the 
copper  core,  with  films  of  non-drying  viscous  adhe- 
sive compound  between  the  layers.  A  separator  is 
sometimes  applied  between  the  copper  core  and  the 


74  ELECTRIC  POWER  CONDUCTORS 

taping,  in  order  to  prevent  any  possible  action  of 
the  varnished  films  on  the  copper. 

This  insulation,  unlike  paper,  does  not  absorb 
moisture  and  may  be  used  for  indoor  work  without 
a  lead  sheath.  It  is  suitable  for  high-tension  cables, 
especially  where  a  lead  sheath  cannot  be  used,  as, 
for  example,  when  subjected  to  vibration.  In  such 
cases  it  is  usual  to  protect  the  insulation  by  a  spiral 
galvanized  steel  tape ;  this  construction  is  not  suitable 
however  for  single  conductor  cables  carrying  alter- 
nating currents. 

Cambric  insulation  is  considerably  more  flexible 
than  paper,  it  being  possible  to  bend  cables  to  a 
radius  of  six  times  their  diameter,  without  injury. 
Unlike  rubber- insulated  cables,  the  insulation  re- 
mains concentric  with  the  core. 

Other  advantages  of  varnished  cambric  are  that 
splices  are  simple,  and  that  mineral  oils  have  no 
effect  upon  it. 

Varnished  cambric  is  the  best  insulation  for  high 
tension  station  wiring,  as  it  can  be  installed  without 
the  metallic  sheath  and  end  bells  required  for  paper 
cable,  while  it  stands  heat,  static  discharges,  and 
overloads  much  better  than  the  best  grade  of  rubber 
insulation. 

Oil  of  the  variety  generally  used  in  switches  and 
in  the  lubrication  of  generators  does  not  injure 
varnished  cambric.  The  cables  can,  therefore,  be 
run  directly  into  oil  switches  and  oil-filled  trans- 


INSULATION  AND  INSULATED  CONDUCTORS    75 

formers,  or  can  be  used  as  leads  to  generators. 
Rubber  cables  when  used  in  similar  circumstances 
are  ruined  in  a  very  short  time. 


FACTOR   FOR   CORRECTION   OF   INSULATION   RESISTANCE 
TO  15.5°  C. 


Temperature, 
Deg.  C. 

Factor  for  Var- 
nished Cambric. 

30 

13.00 

29 

II.OO 

28 

9-35 

27 

8.07 

26 

6.76 

25 

5-92 

24 

5-oo 

23 

4.06 

22 

3-30 

21 

2.76 

2O 

2.32 

19 

2.OO 

18 

1.70 

17 

I.4O 

16 

1.16 

1  5.  5  (60°  F.) 

I.  00 

15 

0.88 

The  resistance  at  15.5°  C.  is  found  by  multiplying 
the  observed  resistance  by  the  factor  corresponding  to 
the  temperature  at  which  the  resistance  is  measured. 


76  ELECTRIC  POWER  CONDUCTORS 


2.  INSULATED   CABLES 

Underground.  Paper  being  the  cheapest  kind  of 
insulation  which  is  permanent,  is  more  extensively 
used  than  any  other  kind  for  underground  work. 
As  long  as  the  sheath  is  intact,  it  is  as  good  as  any 
other  material.  If  the  sheath  is  punctured  either 
mechanically  or  electrolytically  or  any  other  way, 
moisture  penetrates  the  paper  and  grounds  the  con- 
ductor. If  the  cable  is  under  water,  the  zone  affected 
by  water  will  probably  extend  in  both  directions 
from  the  puncture  and  may  necessitate  the  removal 
of  the  cable  length  from  splicing  chamber  to  splicing 
chamber.  In  such  situations,  varnished  cambric  or 
rubber  should  be  used,  preferably  the  former  if  the 
voltage  is  high.  Another  application  of  varnished 
cambric  or  rubber  is  to  direct  current  railway  feeders 
and  third  rail  jumpers  where,  as  explained  below,  a 
lead  sheath  is  undesirable. 

The  cables  which  give  the  greatest  trouble  in 
underground  conduit  lines  are  direct-current  railway 
feeders  of  large  carrying  capacity.  The  reasons  for 
this  are: 

(1)  When  they  are  punctured  the  cable  is  short- 
circuited  to  the  sheath,  and  the  current  is  so  great 
that    the    sheath    is    melted,    often   for    a    length    of 
several  hundred  feet. 

(2)  If  the  direct-current  cable  sheath  is  in  metallic 


•  * 
INSULATION   AND  INSULATED  CONDUCTORS    77 

connection  with  other  sheaths,  the  short-circuit  cur- 
rent will  distribute  itself  among  these  sheaths,  and 
may  melt  them  in  the  same  way  as  the  sheath  of 
the  original  cable. 

(3)  When  cable  sheaths  are  melted  or  burned,  not 
only  are  the  cables  put  out  of  use,  but  it  is  often 
impossible  to  withdraw  them  from  the  ducts,  which 
therefore  have  to  be  broken  into  and  replaced.     If 
this  does  not  occur,  the  lining  of  the  ducts  may  be 
so  roughened  as  to  render  new  ones  necessary. 

(4)  The  arc  established  at  the  point  of  short  circuit 
is  so  intense  as  to  be  a  source  of  danger  to  linemen, 
to  other  cables,  and  to  the  structure  of  the  splicing 
chamber  itself. 

(5)  If  the  short  circuit  occurs  far  from  the  station- 
bus,  the  resistance  of  the  line  may  be  sufficient  to 
keep    the    value    of    the    short-circuit    current    below 
that  at  which  the  circuit  breakers  are  set  to  open. 
Such  short  circuits  are  particularly  dangerous  because 
there  is  no  way  to  distinguish  them  on  the  station 
meters  from  a  regular  load. 

With  these  facts  in  view,  the  following  precautions 
should  be  adopted  with  large  direct-current  cables: 

(i)  Where  possible,  keep  the  direct-current  cables  out 
of  the  duct  lines  which  carry  the  alternating-current 
cables.  It  may  be  advisable  to  put  the  required 
conductivity  in  the  third  rails  in  order  to  avoid  the 
necessity  of  auxiliary  copper  in  duct  lines  along  the 
track. 


78  ELECTRIC  POWER  CONDUCTORS 

(2)  If  it  is  necessary  to  put  direct-  and  alternating- 
current  cables  in  the  same  duct  line  it  is  well  to  isolate 
the  direct-current  cables  as  much  as  possible  in  the 
splicing  chambers.     This  may  be  effected  by  running 
them  in  open-face  ducts,  or  by  protecting  them  with 
split  ducts  put  around  the  cables  and. held  together 
by  clay.     Such  ducts  may  be  supported  on  one  or 
two  light  angle  irons  extending  longitudinally  through 
the  chamber. 

(3)  The  racks  on  which  direct-current  cables  are 
supported    in    splicing    chambers    should    not    be    in 
metallic  connection  with  other  racks.     If,   however, 
this  is  unavoidable,  the  cables  should  not  lay  directly 
on  the  racks,   but  on  insulating  pads  or  blocks. 

(4)  The  electrostatic  charges  on  the  sheaths  of  low- 
tension   cables    are    insignificant,    and   none    can    be 
derived   from    the   high-tension   cables    if    these    are 
properly  grounded.     It  is  therefore  not  necessary  to 
ground   the   sheaths    of   direct-current   cables   of   an 
insulated  system.     With  a  grounded  return  system, 
however,  the  case  is  different,  for  however  well  the 
cable  sheath  is  insulated  in  a  duct  line,  in  the  case 
of  a  short  circuit  the  current  will  find  its  way  through 
tne  most  unexpected  paths,   thereby  creating  wide- 
spread   damage.     As    grounded    return    systems    are 
used  principally  for  railways,   it  is  usual  to  ground 
the  direct-current  cable  sheaths  directly  to  the  track 
rails  through  stout  wires. 

Where  this  is  done,  high  tension  cables  in  the  same 


•    * 
INSULATION  AND  INSULATED  CONDUCTORS    79 

subways  should  not  be  grounded  to  the  track  rails. 
Railroad  tracks  having  insulated  sections  for  auto- 
matic block  signals  cannot  be  used  in  this  way,  as 
the  sections  would  be  electrically  connected  through 
the  cable  sheaths.  In  such  cases,  feeders  should 
either  be  kept  out  of  the  duct  line  or  protected  by 
short  circuit  indicator  wires,  as  described  on  page 

93- 

If   retaining  walls   or   tunnel   walls   are   available, 

it  is,  easy  to  support  weatherproof  cable  on  large 
porcelain  clamp  insulators  attached  to  the  walls. 
In  the  open,  however,  it  is  usually  necessary  to 
support  the  cables  on  insulators  placed  in  a  wooden 
or  concrete  trough,  which  is  filled  with  viscous 
insulating  and  waterproof  compound.  This  is  known 
as  the  "  solid  system." 

Arcs  produced  by  the  rupture  of  alternating- 
current  tables  are  less  intense  than  those  produced 
by  direct-current  cables,  for  the  following  reasons: 

(1)  The  periodic  reversal  of  the  current  tends  to 
extinguish   the  arc  twice  in   every  cycle. 

(2)  The  amperes  per  kilowatt  transmitted  are  less 
than     with     direct-currents,     owing     to     the     high 
voltages     used    in    alternating-current    transmission 
systems. 

(3)  The  use  of  two  or  three  conductor  cables  helps 
to  make  a  clean  short  circuit,  which  will  operate  the 
power-house  relays  at  once  and  thrs  open  the  cir- 
cuit.    It  also  does  away  with  the  tendency  to  follow 


80  ELECTRIC  POWER  CONDUCTORS 

any  roundabout  path  to  ground,  as  with  direct- 
current  cables. 

(4)  The  carrying  capacity  of  the  lead  sheath  of 
a  high-tension  cable  is  usually  great  enough  to  take 
without  injury  sufficient  current  to  operate  the 
relays  in  the  power  station,  especially  where  resis- 
tance is  used  in  the  grounded  neutral  of  the  generators. 

There  is,  however,  a  danger  inherent  to  high- 
tension  cables  which  must  be  carefully  guarded 
against,  namely,  electrostatic  induction. 

When  an  electrically  charged  body  is  introduced, 
without  touching,  into  a  cylindrical  conductor,  a 
charge  is  induced  on  the  inner  surface  of  the  cylin- 
der, which  is  equal  in '  magnitude  but  opposite  in 
sign  to  the  charge  on  the  electrified  body.  If  the 
cylinder  is  insulated  from  the  earth  there  is  also 
induced  on  its  outer  surface  a  charge  of  equal  mag- 
nitude and  similar  sign  to  that  of  the  electrified 
body.  The  difference  of  potentials  between  the 
charged  body  and  cylinder  depends  on  their  dimen- 
sions and  relative  locations,  and  may  be  very  con- 
siderable. If,  however,  the  cylindrical  conductor 
is  connected  to  the  ground  by  a  metallic  wire,  it  will 
be  maintained  at  ground  potential. 

A  high-tension  cable  in  a  lead  sheath  acts  pre- 
cisely like  the  charged  body  in  a  cylindrical  conductor 
described  above,  inducing  a  charge  on  the  sheath 
which  may  raise  the  latter  to  a  dangerously  high 
potential. 


INSULATION  AND  INSULATED  CONDUCTORS    81 

It  is  therefore  necessary  to  ground  the  sheaths 
of  cables  at  intervals,  in  order  to  carry  off  their 
"  static,"  as  the  induced  charge  is  commonly  called. 

Under  Water.  Rubber  is  almost  invariably  used 
for  submarine  power  work  on  account  of  its  absolute 
waterproofness  and  inertness  with  respect  to  salt 
water. 

While  it  is  usual  to  enclose  the  rubber  in  a  lead 
sheath  protected  by  steel  armor,  the  lead  sheath 
may  be  dispensed  with  unless  there  is  sewage  or 
other  injurious  impurities  in  the  water. 

Owing  to  their  inaccessibility  for  repairs,  sub- 
marine cables  should  be  free  from  all  defects  which 
might  give  rise  to  trouble  in  the  event  of  excessive 
current  or  voltages  occurring  in  them.  Such  defects 
are  splices  in  the  conductors,  faulty  patches  in  the 
insulation,  faulty  patches  in  the  sheathing,  injury 
to  sheathing  by  tight  armor,  etc.  These  defects 
should  be  guarded  against  by  careful  inspection  at 
the  factory. 

The  author  has  seen  a  length  of  11,000  volt 
triplex  submarine  cable  supplied  by'  one  of  the 
best-known  manufacturers  in  the  country  in  which 
were  discovered  a  group  of  wire  splices  which  had 
become  loose  in  service,  an  un vulcanized  patch 
in  the  insulation,  and  two  improperly  repaired  splits 
in  the  lead  sheath.  The  cable  broke  down  in  service 
and  was  a  total  loss. 

On   Walls,   etc.,   in   the   Open.     Varnished    cambric 


82  ELECTRIC  POWER  CONDUCTORS 

exposed  to  the  heat  of  the  sun  deteriorates  owing 
to  the  softening  of  the  compound  and  its  conse- 
quent settlement  from  the  upper  part  to  the  lower 
part  of  tlie  cable.  This  phenomenon  occurs  where 
cables  are  laid  either  horizontally  or  vertically.  In 
consequence  of  this,  rubber  is  less  liable  to  give 
trouble  in  exposed  locations.  Paper  is  but  slightly 
affected  by  the  softening  and  flow  of  compound 
where  the  cables  are  horizontal,  but  where  cables 
are  vertical  it  is  likely  to  give  trouble. 

In  House  Conduits.  For  house  wiring,  rubber 
insulation  covered  with  tape  and  braid  is  almost 
invariably  used,  and  except  for  the  larger  sizes  it 
is  practically  alone  in  the  field.  Beginning  with 
No.  6  B.  &  S.  varnished  cambric  is  a  rival  to  the 
rubber  if  the  wire  does  not  have  to  be  pulled  around 
sharp  bends. 

"  Code  "  insulation  is  a  cheap  rubber  compound 
or  substitute  for  rubber  which  is  very  largely  used 
for  house  wiring  and  its  use  is  probably  responsible 
for  the  large  number  of  fires  due  to  defective  insu- 
lation. 

Thickness  of  Insulation.  The  thickness  of  insula- 
tion which  should  be  used  for  a  given  voltage  and 
size,  is  determined  largely  by  experience.  The  dielec- 
tric strength  of  impregnated  cambric  is  so  great 
that  a  very  thin  film  of  this  material,  under  labora- 
tory conditions,  will  suffice  for  most  voltages  in 
practical  use.  An  enormous  factor  of  safety,  how- 


INSULATION  AND  INSULATED  CONDUCTORS   83 

ever,  is  necessary  in  order  to  compensate  for 
inevitable  defects  in  manufacture  and  to  allow 
for  injury  in  handling,  especially  in  bending.  Rub- 
ber, on  the  other  hand,  is  comparatively  weak 
dielectrically,  and  superior  mechanically,  making  the 
calculation  of  thickness  a  possibility.  Table  I  gives 
the  proper  thickness  calculated  according  to  the 
theory  given  in  Appendix  3.  Tables  II  was  prepared 
by  the  engineer  of  an  important  manufacturing  firm. 
Tables  III  and  IV  have  been  adopted  as  standards  by 
the  Rubber  Covered  Wire  Engineers  Association  (1907). 
Table  V  and  its  accompanying  data  were  prepared 
by  Mr.  H.  G.  Stott,  whose  experience  with  paper 
insulated  cables  is  probably  unequalled. 

Table  VI  is  from  a  G.  E.  Co.  bulletin,  and  represents 
the  best  practice  with  varnished  cambric. 

The  thickness  of  insulation  on  cables  for  very 
high  voltages  can  be  considerably  reduced  by  grad- 
ing. The  conductor  is  first  insulated  with  rubber 
and  the  cambric  is  then  applied  to  secure  the  insu- 
lating wall  necessary  for  the  required  test. 

The  width  of  tape  over  the  insulation  is  usually 
equal  to  twice  the  square  root  of  the  cable  diameter 
over  the  insulation. 


84 


ELECTRIC   POWER  CONDUCTORS 


TABLE  I 

THICKNESS  OF  RUBBER  INSULATION,  64xHs  INCH 
1  See  Appendix  III 


Single  Phase  Volts  between  Conductor  and  Sheath. 

710- 

2300- 

3900- 

6700- 

Size. 

Number  of 
Strands. 

Direct 
Current. 

Three  Phase  Volts  between  Conductors. 
Thickness  of  Insulation  around  each 
Conductor. 

Up  to  loooV 

4000- 

6750- 

11500- 

B.  &S. 

• 

14 

I 

3  or4 

10 

12 

I 

3  or  4 

8 

IO 

I 

3  or  4 

7 

8 

7 

4 

7 

14 

6 

7 

4 

7 

12 

4 

7 

4 

7 

II 

25 

2 

J9 

4 

7 

II 

22 

I 

*9 

5 

7 

II 

20 

0 

*9 

5 

7 

10 

19 

00 

J9 

5 

7 

10 

18 

000 

19 

5 

7 

10 

18 

oooo 

19 

6 

7 

IO 

18 

Millions  of 

Circ.  Mils. 

0-25 

37 

6 

8 

IO 

!7 

°-35 

61 

7 

8 

II 

17 

o-5 

61 

7 

8 

II 

17 

o-75 

91 

8 

I.O 

9i 

9 

1-25 

127 

10 

i-5° 

127 

10 

i-75 

127 

ii 

2.  CO 

133 

12 

Stranding,  concentric,  except  for  2,000,000  C.M.,  which  is  rope. 


INSULATION  AND  INSULATED  CONDUCTORS   85 


TABLE  II 

RUBBER  INSULATION 

Puncture  Tests  (30%  Para  Compound 
Low  POTENTIAL,  600  VOLTS 


B.  &  S.  Gauge. 


Wall. 


Voltage 
Test  for 
i  Minute. 


Nos.  14  to  8 3/64  in. 

6  to  2 4/64  ' ' 

I  to  4/0 5/04 

250,000  to     500,000  cir.  mils 6/64  " 

550,000  to  1,000,000       "          7/64" 

MEDIUM  POTENTIAL,  3500  VOLTS 

Nos.  14  to  8 3/32  m- 

"       6  to  2 3/32  " 

"     i  to  4/0 3/32  " 

250,000  to      500,000  cir.  mils 3/32  ' 

550,000  to  1,000,000         "        4/32  ' ' 

5000  VOLTS  WORKING  PRESSURE 

Nos.  4  to  4/0 6/32  in. 

250,000  to      500,000  cir.  mils 6/32  " 

550,000  to  1,000,000         "        6/32" 

11,000  VOLTS  WORKING  PRESSURE 

Nos.  4  to  4/0.  . 9/3"  in- 

250,000  to      500,000  cir.  mils 9/3-  " 

550,000  to  1,000,000         "        9/32  " 

Nos.  4  to  4/0 10/32  in. 

250,000  to      500,000  cir.  mils 10/32  " 

550,000  to  1,000,000         "        10/32" 

Nos.  4  to  4/0 12/32  in. 

250,000  to  500,000  cir.  mils 12/32  " 

550,000  to  1,000,000    "   12/32  " 


1,000 
1,000 
1,000 
1,000 
1,000 


5,000 
5,000 
5,000 
5,000 
5,000 


10,000 

10,000 

10,000 


15,000 
15,000 
15,000 

20,OCO 
20,000 
20,000 

20,OOO 
20,OOO 
20,000 


J.  Langan,  Am.  Inst.  Elect.  Eng.,  1506. 


86 


ELECTRIC  POWER  CONDUCTORS 


TABLE  III 

RUBBER    INSULATION 

MEGOHMS  PER  MILE.    60°  F.     ONE  MINUTE  ELECTRIFICATION 


Thickness  of  insulation  in  inches. 

3/64. 

2/32. 

5/64. 

3/32. 

7/64. 

4/32. 

5/32. 

6/32. 

7/32. 

8/32. 

C.M. 
1,000,000 

7QO 

340 

42O 

4QO 

t;6o 

6^0 

900,000 

320 

360 

440 

510 

590 

660 

800,000 

33° 

380 

460 

540 

610 

690 

700  ooo 

•?c,o 

4OO 

40O 

C,7o 

6  co 

73O 

600  ooo 

^80 

C2O 

*77O 

500  ooo 

"?6o 

4IO 

46O 

£.70 

660 

7c.o 

830 

400,000 

4OO 

4^O 

CIQ 

620 

72O 

820 

OIO 

•2QO  OOO 

4Co 

r  20 

s8o 

7OO 

810 

910 

2  Co  OOO 

4QO 

$60 

620 

7  CO 

870 

980 

1090 

4/0  Strand 

4^0 

^30 

610 

680 

820 

040 

1060 

Ii7o 

3/0  Strand 

500 

^90 

670 

740 

800 

IO2O 

II  <O 

1270 

2/0  Strand 

^60 

6zo 

740 

820 

080 

1  1  3O 

1  260 

1^80 

i  /o  Strand 

600 

710 

800 

890 

1060 

I2IO 

13^0 

1470 

i  Solid 

75° 

870 

97° 

1080 

1270 

I44O 

1600 

1740 

2  Solid 

680 

820 

Q<O 

1070 

1170 

1380 

i  ^60 

1  720 

1870 

3  Solid 

750 

900 

1040 

1160 

1280 

1490 

1680 

1850 

20OO 

4  Solid 



820 

980 

1130 

1260 

1380 

1610 

1800 

1980 

2I4O 

5  Solid 



910 

1070 

1230 

T37° 

1500 

1740 

1940 

2130 

2290 

6  Solid 



990 

1160 

!33° 

1480 

1610 

1860 

2070 

2260 

2430 

8  Solid 

95° 

1170 

J37o 

1560 

1720 

1870 

2140 

2360 

2570 

2750 

9  Solid 

1040 

1280 

1490 

1680 

1850 

2000 

2280 

2520 

2730 

2910 

10  Solid 

1130 

1390 

1610 

1810 

1990 

2150 

2440 

2680 

2890 

3000 

12  Solid 

1340 

T620 

1860 

2080 

2270 

2440 

2750 

3000 

3220 

3420 

14  Solid 

i55° 

1860 

21  2O 

2360 

2560 

2740 

3060 

33  20 

355° 

3750 

Rubber  Covered  Wire  Engineers  Association  (1907). 


INSULATION  AND  INSULATED  CONDUCTORS   87 


TABLE  IV 

VOLTAGE  TEST  FOR  FIVE  MINUTES 

FOR  30  MINUTES  TEST,  TAKE  80%  OF  THESE  FIGURES 


Size. 

Thickness  of  Insulation  in  Inches. 

3/64- 

2/32- 

5/64. 

3/32. 

7/64. 

4/32. 

5/32. 

6/32. 

7/32. 

8/32. 

1,000,000  to 
550,000 
500,000  to 
250,000 
4/0  to  i 
2  to  7 
8  to  14 

r 

6000 

7000 

8000 
9000 
9000 

8000 

90OO 

IOOOO 
1  1  000 
IOOOO 

12000 

I3OOO 

13000 
14000 
IIOOO 

I6OOO 

I6OOO 

16000 
16000 
I200O 

19000 

19000 

I9OOO 
18000 

22000 

22000 

22000 
2OOOO 

\  " 
/ 

50OO 

600O 
70OO 
7500 

i  " 

40OO 
5OOO 
600O 

3000 
4500 

3000 

Rubber  Covered  Wire  Engineers  Association  (1907). 

Thickness  of  Insulation  (Paper).  "  As  the  result  of 
some  fifteen  years  of  experience  with  underground 
cables,  the  following  table,  giving  thickness  of  insu- 
lation and  lead  sheath  for  various  sizes  of  conductors 
and  working  pressures,  is  submitted  as  representing 
conservative  practice: 

TABLE  V 

PAPER  INSULATION 
STANDARD  WORKING  PRESSURE  OF  4000  VOLTS 


Size  of  Conductors. 

Thickness  of 
Insulation. 

Thickness  of  Lead. 

Single  Cond. 

Three  Cond. 

Nos.  6  to  2  B.  &  S    

5/32  in. 
5/32' 
6/32' 
6/32' 
6/32  < 
7/32  ' 

5/64  in. 
3/32  " 
7/64" 

7/64" 
4/32-" 
9/64" 

3/32  in. 
7/64" 
9/64  « 

'  '     i  to  oo    '  ' 

No.  ooo  to  300,000  cm.  . 

400,000  to     750,000  cm  

800,000  to  1,000,000   " 

1,250,000102,000,000   "    

88  ELECTRIC  POWER  CONDUCTORS 

"For  each  1000  volts  increase  of  pressure  above 
4000  add  1/32-in.  insulation  to  the  wall  until  11,000 
volts  is  reached,  and  after  that  add  1/64  in.  for 
each  1000  volts.  For  example,  the  insulation  re- 
quired on  a  No.  o  B.&S.  25,ooo-volt  cable  would  be 
19-32  in.  If  35%  Para  rubber  compound  or  varnished 
cambric  is  used  for  insulation  the  above  empirical 
rule  may  be  changed  to  read:  for  each  1000  volts 
increase  above  3000,  add  1/64  in.  insulation  to  the 
thickness  of  wall  until  25,000  volts  is  reached.  For 
the  insulation  of  low-potential  cables,  4/32  in.  paper 
should  be  used  on  all  sizes  up  to  1,000,000  cm.,  and 
from  1,250,000  to  2,000,000  cm.,  5/32  in.  should  be  used. 

"  From  a  purely  electrical  point  of  view,  one-half 
of  this  insulation  would  be  ample  to  withstand  650 
volts  working  pressure,  but  the  mechanical  effects  of 
reeling  and  unreeling  the  cable  and  pulling  it  into 
ducts  and  bending  around  the  manholes,  are  to 
practically  destroy  the  insulating  qualities  of  the 
layer  of  paper  next  the  lead,  so  that  we  really  start 
in  with  a  cable  having  approximately  */32  in.  of  its 
insulation  destroyed  before  it  is  put  into  commission; 
this  mechanical  destruction  of  insulation  is  especially 
marked  in  cold  weather,  as  the  oils  used  with  the 
paper  tend  to  congeal  when  subjected  to  a  tempera- 
ture below  32°  F.  The  cable  manufacturers  have 
met  this  difficulty  by  using  more  fluid  oil,  with  the 
result  that  the  insulation  resistance  of  the  cable  may 
not  be  more  than  50  megohms  at  60°  F.,  but  by 
the  use  of  this  very  soft  insulation  they  have  pro- 


INSULATION  AND  INSULATED  CONDUCTORS    89 

duced  a  cable  giving  a  very  low  insulation,  but  a 
high  puncture  test,  and  at  the  same  time  have  met, 
to  a  great  extent,  the  difficulty  of  handling  paper 
cable  in  cold  weather.  It  is  always  advisable,  how- 
ever, if  a  cable  is  to  be  used  in  a  temperature  below 
32°  F.,  to  keep  it  in  a  warm  place,  such  as  a  boiler- 
room,  for  at  least  twelve  hours  before  drawing  it  in. 
The  cable  may  then  be  used  in  the  coldest  weather, 
as  it  gives  up  its  heat  very  slowly."  (H.  G.  Stott, 
Am.  Street  and  Interurban  Ry.  Assoc.,  Oct.,  1906.} 


The  working  voltages  in  Table  VI  are  based  on  all 
conductors  of  the  circuit  being  insulated.  For  direct- 
current  6oo-volt  railway  single  conductor,  leaded  cables, 
use  2ooo-volt  class.  For  three-phase  "  Y  "  connected 
circuits  with  grounded  neutral  with  three  conductor 
cables,  thickness  of  insulation  between  conductors 
and  ground  need  only  be  7/io  of  that  between  con- 
ductors. Tests  on  such  cable  in  proportion  to  thick- 
ness of  insulation;  Example,  three-phase,  i2,ooo-volt 
circuit  "  Y,"  neutral  grounded,  insulation  on  each 
conductor  6/32  in.  (total  between  conductors  12/32  in.), 
outer  belt  3/32  in.  (total  9/32  in.) ;  test  pressure  at  fac- 
tory for  five  minutes  between  conductors  30,000 
volts,  each  conductor  to  earth  22,500  volts.  For 
mechanical  reasons,  thickness  of  insulation  on  individual 
conductors  of  three-conductor  cables  3000  volts  and 
less  is  made  somewhat  greater  than  required  by  work- 
ing pressure  on  some  sizes. 


90 


ELECTRIC  POWER  CONDUCTORS 


TABLE  VI 

WORKING  AND  TEST  VOLTAGES 
VARNISHED  CAMBRIC 


Kilo 
Volts 
Work- 
ing 
Pres- 
sure. 

Sizes. 

Thick- 
ness 
Insula- 
tion. 

TEST  IN  KILO  VOLTS 

At  Factory. 

After  Installation. 

5 
min. 

30 

min. 

60 
min. 

j 

min. 

3° 
min 

60 

min. 

I 

6-2 

1/16 

2-5 

2 

.6 

2 

.6 

!-3 

I 

I  -0000 

5/64 

2-5 

2 

.6 

2 

.6 

1-3 

I 

250,000-500,000 

3/32 

2-5 

2 

.6 

2 

.6 

i-3 

I 

550,000-1,000,000 

7/64 

2-5 

2 

.6 

2 

.6 

J-3 

I 

1,100,000  and  over 

4/32 

2-5 

2 

.6 

2 

.6 

i-3 

2 

6-0000 

3/32 

5- 

4 

3-2 

4 

3-2 

2.6 

2 

250,000-500,000- 

7/64 

5- 

4 

3-2 

4 

3-2 

2.6 

2 

550,000-2,000,000 

4/32 

5- 

4 

3-2 

4 

3-2 

2.6 

3 

All  sizes 

9/64 

7-5 

6 

4.2 

6 

4.8 

3-8 

4 

«  « 

•5/32 

10. 

8 

6.4 

8 

6.4 

5-i 

5 

(  C 

6/32- 

12.5 

10 

8. 

10 

8. 

6.4 

6 

(  ( 

7/32 

15- 

12 

9.6 

12 

9.6 

7-7 

7 

« 

8/32 

17-5 

14 

II.  2 

14 

IT.  2 

9.0 

8 

<  ( 

17/64 

20. 

16 

12.8 

16 

12.8 

10.2 

9 

<  < 

9/32 

22-5 

18 

14.4 

18 

14.4 

"•5 

10 

" 

10/32 

25- 

20 

16. 

20 

16. 

12.8 

ii 

<  ( 

II/32 

27-5 

22 

17.6 

22 

17.6 

14.1 

12 

(  ( 

12/32 

3°- 

24 

19.2 

24 

19.2 

15-4 

13 

<  ( 

12/32 

32.5 

26 

20.8 

26 

20.8 

16.6 

14 

1  1 

13/32 

35- 

28 

22.4 

28 

22.4 

17.9 

15 

11 

13/32 

37-5 

3<> 

24. 

3° 

24.0 

19.2 

16 

11 

14/32 

40. 

32 

25.6 

32 

25.6 

20.5 

17 

<  I 

14/32 

42.5 

34 

27.2 

34 

27.2 

21.7 

18 

1  ' 

15/32 

45- 

36 

28.8 

30 

28.8 

23.0 

J9 

<  « 

15/32 

47-5 

38 

3°-4 

38 

3°-4 

24-3 

:o 

" 

16/32 

So. 

40 

32- 

40 

32. 

25-5 

21 

(  C 

l6/32 

52.5 

42 

33-6 

42- 

33-6 

26.8 

22 

<  < 

17/32 

55- 

44 

35-2 

44 

35-2 

28.! 

23 

(  ( 

17/32 

57- 

46 

36.8 

46 

36.8 

29.4 

24 

1  1 

18/32 

60. 

48 

38.4 

48 

38.4 

3°-7 

25 

tl 

18/32 

62.5 

5° 

40. 

50 

40. 

3i-9 

G.  E.  Bulletin  4591- 


I 

INSULATION  AND  INSULATED  CONDUCTORS     91 

Belted  and  Unbelted  Triplex  Cable.  In  a  three- 
conductor  cable  for,  say,  11,000  volts,  the  insulation 
can  be  most  advantageously  disposed  if  each  con- 
dutor  is  insulated  for  half  of  11,000,  i.e.,  5500  volts, 
and  the  group  insulated  by  a  belt'  good  for  900  volts, 
this  being  the  difference  between  5500  and  6400, 
the  voltage  from  conductor  to  ground.  A  triplex 
cable  built  on  this  plan,  i.e.,  with  an  exterior  belt, 
is  therefore  dielectrically  the  strongest  as  long  as  the 
belt  is  intact.  For  this  reason  paper  insulated  cables 
are  almost  invariably  of  the  belted  type. 

Rubber  cables  differ  from  paper  in  not  necessarily 
breaking  down  when  the  sheath  is  punctured.  It  is 
therefore  desirable  to  design  such  cables  so  that  they 
will  not  be  put  out  of  service  in  the  event  of  water 
getting  at  the  insulation.  When  a  triplex  cable  of 
the  belt  type  is  punctured  so  as  to  admit  water  under 
the  belt,  the  whole  surface  under  the  belt  and  between 
conductors  becomes  rilled  with  water  for  a  consider- 
able distance  on  each  side  of  the  puncture,  perhaps 
even  for  the  whole  length  of  the  cable.  The  result 
of  such  a  puncture  is  to  put  a  stress  of  6400  volts  on 
the  5500  volt  insulation.  The  puncturing  of  a  sheath 
of  an  unbelted  triplex  cable  is  attended  with  no  such 
injurious  result,  and  if  the  insulation  of  only  one 
conductor  is  injured,  the  other  two  are  intact.  The 
former  may  be  used  if  supplemented  by  a  new  single 
conductor  cable  or  by  a  similar  uninjured  wire 
from  another  injured  cable. 


92  ELECTRIC  POWER  CONDUCTORS 

The  processes  of  manufacture  of  belted  triplex 
cables  with  rubber  insulation  also  place  this  type  at 
a  disadvantage  compared  with  the  unbelted  type. 
The  insulation  on  the  individual  conductors  being 
vulcanized  and  tested  before  the  conductors  are 
assembled  is  subjected  to  an  additional  cooking  when 
the  belt  is  vulcanized.  This  is  liable  to  alter  its 
electrical  and  mechanical  characteristics  after  test, 
which  is  very  undesirable. 
Diameter  of  a  Triplex  Cable. 

Let      d  =  diameter  of  each  conductor ; 

t=  thickness  of  insulation  around  each  con- 
ductor ;    , 
T  =  sum  of  thickness  of  sheath  and  outer  belt 

of  insulation,  if  any. 
Diameter  -  2.  i  $d  +  4.3*  +  2  T. 

Thickness  of  Sheath.  The  following  sheath  thick- 
nesses are  recommended  as  representing  the  best 
practice  for  cables  in  tile  ducts: 

„.  Thickness  of  Sheath. 

Inches. 

14-8  B.  &  S 3/64 

6-1   B.  &  S 4/64 

o  B.  &  S.  to  250,000  cm 5/64 

500,000  to  750,000  cm 6/64 

1,000,000  cm 7/64 

1,250,000—2,000,000  cm 8/64 

Triplex-ooo  B.  &  S 8/64 

Triplex-oooo  B.  &  S 9/64 


INSULATION   AND  INSULATED  CONDUCTORS     93 


Short  Circuit  Indicator.  Direct-current  feeders  fed 
through  circuit  breakers  set  for  large  currents  may 
be  protected  against  the  effects  of  short  circuits  by 
means  of  the  following  device: 

The  automatic  relay  feature  of  the  circuit  breaker 
is  connected  to  a  small  wire  or  a  pair  of  wires  clipped 
or  taped  to  the  feeder  cable  along  its  entire  length 
in  such  a  way  that  a  short  circuit  will  burn  these 
wires  and  thereby  open  the  relay  circuit.  The  relay 
is  of  the  low  voltage  release  type,  so  that  the  inter- 
ruption of  its  circuit  has  the  effect  of  promptly  open- 
ing the  circuit  breaker.  A  diagram  of  connections  is 
shown  in  Fig.  8. 


*-  Cable 


FIG.  8. 

A  No.  12  B.  &  S.  wire  with  ^  in.  30%  Para  rub- 
ber compound  taped  and  braided  is  usually  suitable 
for  this  service,  but  the  correct  size  should  be  worked 
out  for  each  installation,  taking  into  account  both 
the  carrying  capacity  and  potential  drop.  The  fuse 
on  the  negative  side  comes  into  service  in  case  the 
short  circuit  melts  the  indicator  wire  into  contact 
with  the  main  feeder  metal  thereby  maintaining  the 


94  ELECTRIC   POWER  CONDUCTORS 

continuity  of  the  circuit.  In  such  a  case,  the  rush 
of  current  to  ground  blows  the  fuse  and  interrupts 
the  relay  circuit.  This  system  has  been  in  suc- 
cessful operation  on  the  New  York  Central  R.  R.  to 
protect  feeders  along  the  Park  Avenue  viaduct  and 
tunnel.  It  was  devised  by  the  author  early  in  1906, 
and  is  unpatented. 


3.  INSULATORS,  PINS,  ETC. 

REQUIREMENTS  OF  A  GOOD  INSULATOR 

1.  Dielectric  strength. 

2.  Resistance  to  surface  arcing. 

3.  Mechanical  strength. 

4.  Ease  of  erection. 

5.  Facility  of  cleaning. 

6.  Negligible    electrostatic     capacity,     this     oemg, 
however,   the  least  important   qualification. 

Dielectric  Strength.  This  quality  is  affected  by 
dielectric  strength  of  material,  by  thickness  of  mate- 
rial, and  by  freedom  from  flaws. 

Porcelain  and  glass  are  the  omy  materials  used 
extensively,  although  there  are  several  composi- 
tions which  have  had  success  particularly  for  low 
tension  work.  Porcelain  is  almost  universally  used 
for  high  tension  work,  notable  exceptions,  however, 
being  the  use  of  glass  for  57,000  volts  by  the 
Missouri  River  Power  Company,  and  for  40,000 


•   * 
INSULATION  AND  INSULATED  CONDUCTORS     95 

volts  by  the  Madison  River  Power  Company,  Butte, 
Montana. 

A  thick  head  adds  to  the  dielectric  strength  but 
reduces  the  mechanical  strength.  The  "  Italian  " 
type  is  solid  and  is  provided  with  a  wide  petticoat 
at  each  end  and  two  small  intermediate  petticoats. 
The  usual  American  practice  for  high  tension  work 
is  to  make  the  insulator  in  two  or  more  pieces,  each 
individually  tested  and  assembled  with  litharge  and 
glycerine  cement.  This  construction  adds  consid- 
erably to  the  dielectric  strength. 

Porcelain  which  absorbs  water  should  be  avoided, 
although  it  is  not  uncommon  to  find  an  absorption 
of  i%  or  2%  in  commercial  porcelain.. 

Resistance  to  Surface  Arcing.  This  quality  is 
affected  by  material,  texture  of  surface,  and  shape 
of  insulator. 

With  regard  to  material,  porcelain  is  universally 
conceded  to  be  superior  to  glass  on  account  of  its 
less  hygroscopic  nature.  The  surface  should  be 
very  smooth  and  uniform. 

The  shape  is  a  matter  of  great  importance,  and 
there  is  a  division  of  opinion  as  to  the  relative  merits 
of  many  petticoats  or  a  wide  umbrella  or  bell  com- 
bined with  a  long  pin  shield.  Petticoats  give  long 
leakage  surface  but  shorter  arcing  distance,  and 
are  more  difficult  to  manufacture. 

Mechanical  Strength.  Mechanical  strength  depends 
upon  strength  of  material,  thickness  of  material,  and 


96  ELECTRIC  POWER  CONDUCTORS 

judicious  design.  Porcelain  is  superior  to  glass 
mechanically,  and  glass  is  more  subject  to  internal 
stresses  developed  in  manufacture.  Glass,  however, 
being  transparent,  has  the  advantage  of  enabling 
flaws  to  be  readily  detected. 

Facility  of  Cleaning.  Facility  of  cleaning  depends 
upon  the  size  of  spaces  between  petticoats.  The  bell 
and  shield  type  is  decidedly  superior  to  the  petticoat 
type  in  this  characteristic.  Glass  in  some  cases 
has  the  advantage  of  permitting  inspection  more 
readily  on  account  of  its  transparency.  The  trans- 
parency has  the  further  advantage  of  preventing 
insects  from  building  cocoons  under  the  petticoats. 

Electrostatic  Capacity.  An  insulator  in  service 
acts  as  the  dielectric  of  a  condenser,  the  two  con- 
ductors of  which  are  the  wire  and  pin.  The  capacity 
of  the  insulator  should  be  as  low  as  possible  to 
minimize  operating  troubles.  This  can  be  accom- 
plished by  having  a  considerable  thickness  of  insu- 
lation between  line  and  pin,  precaution  being  taken 
to  distribute  the  potential  so  as  to  make  each  shell 
carry  its  share  of  the  potential  stress.  In  fact,  a 
multipart  insulator  acts  as  several  condensers  in 
series,  the  voltage  stress  in  the  different  shells  being 
dependent  upon  the  relative  capacities  of  the  several 
condensers. 

Shape.  In  a  severe  rainstorm  the  wind  and 
spattering  from  the  top  surfaces  of  shells  are  liable 
to  wet  practically  all  of  the  insulator  surfaces, 


* 
INSULATION  AND  INSULATED  CONDUCTORS     97 

except  possibly  the  under  surface  of  the  inner  shell. 
In  order  to  keep  this  inner  surface  dry,  the  insulator 
must  be  carefully  mounted  with  respect  to  the 
cross-arm.  The  ideal  multipart  insulator  of  the 
umbrella  type  should  therefore  have  its  inside  shell 
so  designed  that  alone  it  can  carry  the  full  line  poten- 
tial without  puncture  or  arcing.  This  condition 
usually  obtains  on  low  voltage  insulators  but  seldom 
on  those  for  60,000  volts  or  more. 

With  a  given  diameter  and  height,  maximum 
sparking  distance  between  adjacent  rim  and  shell 
can  be,  obtained  by  using  the  curved  type  of  shell, 
but  there  is  a  point  where  this  advantage  is  counter- 
balanced by  the  increased  risk  of  spattering  from 
the  other  shells.  The  flare  of  the  shell  is  often 
determined  by  a  radius  taken  about  the  rim  of 
the  upper  shell  as  center,  the  curve  beginning  at  the 
hypothetical  dry  line,  assuming  that  the  rain  falls 
at  an  angle  of  30°  from  the  horizontal. 

TEST  VOLTAGE  FOR  INSULATORS 

Dry  Test,  insulator  assembled  on  metal  pin ;  fifteen 
minutes  at  three  times  line  voltage. 

Wet  Test,  precipitation  J  in.  per  minute,  45°  angle 
spray  nozzle;  fifteen  minutes  at  i^  times  line  voltage. 

Puncture  Test,  for  each  shell;  fifteen  minutes  at 
from  J  to  ij  times  line  voltage,  the  former  figure  for 
high  voltages  and  the  latter  for  low  voltage. 


98  ELECTRIC  POWER  CONDUCTORS 

By  line  voltage  is  meant  the  normal  voltage  between 
line  and  ground. 

INSULATION  FACTORS 

Wet 

Ratio   of  Arcing   Distance       — .     This    ratio    varies 

Dry 

from  0.3  to  0.9,  averaging  between  0.6  and  0.7 

Ratio  of  Dry  Creeping  Surface  with  45°  Rain  and  Dry. 

This  ratio  varies  from  0.5  to  0.85  and  averages  be- 
tween 0.75  and  0.7. 

Working  Volts  per  Inch  Thickness  of  Insulation. 
Above  10,000  volts  this  varies  between  20,000  and 
60,000,  averaging  between  30,000  and  40,000.  Below 
10,000  volts  mechanical  considerations  settle  the 
thickness. 

Factor  of  Safety  (ratio  of  breakdown  to  working 
volts).  Above  20,000  volts  the  factor  of  safety  varies 
between  2j  and  3  dry,  and  between  ij  and  2^  wet. 
At  voltages  around  10,000  the  factor  is  usually  be- 
tween 6  and  8  dry  and  between  3  and  6  wet. 

Puncturing  Voltage  of  Porcelain.  C.  J.  Greene 
(Eke.  Rev.,  Lond.,  Apr.  24,  1908)  says  that  the  average 
puncturing  voltage  of  porcelain  tested  by  him  is 
approximately  100  kv.  per  inch. 

LINK  INSULATORS 

The  insulator  consists  of  a  solid  porcelain  piece 
having  a  flanged  rim  which  affords  a  long  creepage 
surface  between  live  parts  and  insures  some  portion 


INSULATION  AND  INSULATED  CONDUCTORS     99 

of  the  surface  sheltered  from  rain.  There  are  two 
interlinked  holes  in  the  center  (Fig.  9)  through  which 
the  cables  or  guy  wires  are  threaded,  thereby  bring- 
ing a  compressive  strain  on  the  porcelain. 

An  insulator  of  10  in.  diameter  is  suitable  for  25,000 
volt  service  and  a  6V  in.  insulator  for  12,000  volts. 
For  higher  voltages,  several  disks  are  used  in  series 
spaced  at  a  distance  approximately  equal  to  their 
diameter. 


FIG.  9. — Cross  Section  of  Link  Strain  Insulator. 

The  advantages  of  this  tvpe  of  insulator  are  as 
follows : 

(1)  The  material  is  subjected  on_y  to  compress- ve 
strains. 

(2)  By  the  use  of  the  proper  number  of  insulators 
in  series  practically  any  line  voltage  can  be  used. 

(3)  High   factor   of   safety   both   electrically   and 
mechanically. 


100 


ELECTRIC  POWER  CONDUCTORS 


(4)  Less  likelihood  of  torsional  strains  in  cross  arms 
in  the  event  of  a  wire  breaking. 
The  chief  disadvantages  are: 

(1)  Increased  height  of  poles  or  towers. 

(2)  Necessity  of    frequent    anchoring   of    the   line 
wire. 


FIG.  10. 

Where  several  discs  are  used  in  series,  they  should  be 
linked  together  by  hard  drawn  copper  cable  held  fast 
by  bolted  clamps.  Brass  wire  has  been  tried  and  found 
unsuitable  on  account  of  its  uneven  structure,  and 
galvanized  steel  has  been  found  to  deteriorate  rapidly. 


INSULATION  AND  INSULATED  CONDUCTORS    101 


PINS 

Wooden  pins  are  largely  used  for  low-tension 
work,  but  are  now  considered  risky  for  high-tension 
lines.  The  most  approved  type  of  pin  is  that  of  the 
Long  Island  R.  R.,  a  malleable  cast-iron  pin  which 
it  attached  to  the  cross  arm  by  a  U  bolt  passing 
around  the  cross  arm,  as  shown,  in  Figs.  10  and  n. 


Insulator  Pin  for  H.  T.  Lines.     Long  Island  R.  R.  Type. 
Scale  \  Full  Size.     Dimensions  approx.  only. 

FIG.   II. 

This  construction  obviates  the  drilling  of  holes  in 
the  cross  arms.  The  advantages  of  metallic  pins  are 
long  life,  and  if  grounded,  rapid  and  clean  short 
circuit  in  the  event  of  an  insulator  failing,  thereby 


102 


ELECTRIC  POWER  CONDUCTORS 


preventing   protracted    arcing   and    operating   circuit 
breakers  with  certainty 

Locust    and    eucalyptus    are    the    most    approved 
kinds  of  wood  for  insulator  pins. 


PROPOSED     STANDARD  PINS 
(See  Fig.  12.) 


A. 

7?. 

c 

C 

D. 

£. 

F. 

C. 

H. 

7. 

Nom- 

Act- 

inal. 

ual. 

5 

4f 

4* 

I§ 

iM 

iA 

I| 

I 

i 

if 

»i 

7 

6f 

4* 

if 

ifi 

itt 

«i 

9 

81 

4i 

if 

iff 

itf 

ri 

N 

| 

2 

£ 

N 

2l 

i 

N 

ii 

iof 

4f 

2 

i|J 

itt 

2| 

"fl 

13 

xa| 

4| 

2f 

2& 

2^ 

13 

9 

"rt 

»i 

15 

15 

I4l 

4f 

»J 

2^ 

2^ 

e 

J| 

<2 

2i 

5 

17 
*9 

i6| 

i8f 

Si 

Si 

2f 

2* 

2^ 
2M 

2^ 

2^ 

0) 

1 

0) 

1 

0) 

1 

2j 

2j 

• 

1 

Trans.  Am   Inst.  E.  E.,  vol.  XX,  p.  415. 


FIG.  12. 

CONDUCTIVITY  OF  ATMOSPHERE  AT  HIGH  VOLTAGES 

(From  Amer.  Inst.  Elec.  Eng.,  1904,  H.  J.  Ryan.) 

E  =  maximum   value   of   voltage   curve    (to   obtain 

R.M.S.  value  divide  by  V 2) ; 
r=  radius  of  conductor,  inches; 
5=  distance  between  conductors,  center  to  center; 
D  =  strength  of  electrostatic  field,  coulombs  per  sq.in., 
causing  atmospheric  rupture. 


*•  * 


INSULATION  AND  INSULATED  CONDUCTORS    103 

d=  distance  from  the  surface  of  the  conductor  at 
which  atmospheric  rupture  is  initially  caused. 

E  =  2055  logw(^D(r+d)  X 10™. 

The  following  table  gives  the  relation  between  d, 
D',  and  r  at  a  pressure  of  29.5  in.  of  mercury  and  a 
temperature  of  70°  F. : 


B.  &  S.  Gauge. 

27". 

d. 

D. 

20 

0.03196 

0.0050 

35oXio~10 

15 

0.05706 

O.OIOO 

300 

10 

0.10189 

0.0180 

275 

8 

0.12849 

0.0220 

258 

6 

0.16202 

0.0350 

200 

4 

0.20431 

0.0700 

171 

2 

0.25763 

0.0700 

170 

up  to  625  in.  diam. 

O.C7OO 

I7O 

Amended  to  allow  for  barometric  pressure  and 
temperature,  the  above  formula  reduces  to  the  follow- 
ing, in  which  b  =  barometric  pressure  in  inches  of 
mercury,  and  t=  temperature,  F.  deg., 

17.946 

459  +  * 

If  the  surface  of  the  wire  is  rough,  the  voltage  at 
which  it  glows  is  less  than  given  above. 

Experiments  of  R.  D.  Mershon  at  Niagara  give  the 
critical  voltage  approximately  40%  less  than  the  values 
calculated  from  Ryan's  formula.  (See  Proc.  Am.  Inst. 
Elect.  Eng.  June  30,  1908.) 


CHAPTER  IV 
DETERMINATION   OF   SIZE   OF  CONDUCTORS 

i.    VOLTAGE  AND  SYSTEMS  OF  DISTRIBUTION 

GENERAL  IMPORTANCE  OF  HIGH  VOLTAGE 

The  amount  of  copper  required  to  transmit  a  given 
amount  of  power  at  a  given  loss  over  a  given  dis- 
tance, other  things  being  equal,  is  inversely  pro- 
portional to  the  square  of  the  potential  used,  whatever 
the  system  of  distribution. 

Comparison  of  the  different  systems,  such  as  two- 
wire  single  phase,  three-wire  three-phase,  and  quarter- 
phase  is  given  below  on  the  basis  of  equality  of 
power  delivered,  loss  and  potential. 

In  low-potential  circuits,  as  secondary  networks, 
where  the  potential  is  not  limited  by  the  insulation 
strain  in  the  transmission  system  but  by  the  potential 
of  the  apparatus  connected  into  the  system,  as,  for 
example,  incandescent  lamps,  the  proper  basis  of 
comparison  is  equality  of  the  potential  per  branch 
of  the  system,  or  per  phase. 

On  the  other  hand,  in  long  distance  transmission 
where  the  potential  is  not  restricted  by  any  con- 

104 


DETERMINATION  OF  SIZE  OF  CONDUCTORS    105 

sideration  of  apparatus  suitable  for  a  certain  maxi- 
mum potential  only,  but  where  the  limitation  of 
potential  depends  upon  the  proper  insulation  of  the 
conductors  against  disruptive  discharge,  the  correct 
comparison  is  on  the  basis  of  equal  maximum 
dielectric  strain  on  the  insulation;  for  overhead  lines 
this  means  equality  of  potential  to  ground  as  it  is 
between  ground  and  wire  that  the  insulation  (other 
than  air)  has  to  be  provided. 


COMPARISON  OF  SYSTEMS  WITH  EQUAL  EFFECTIVE  DIF- 
FERENCE OF  POTENTIAL  ACROSS  BRANCH  OR  PHASE 
OF  LOWEST  DIFFERENCE  OF  POTENTIAL 


No. 

of 

Wires 


System. 


Relative 

Amount  of 

Copper. 


c.   or  single-phase,   neutral  full 
c.  or  single-phase,  neutral  half 


Continuous  current.  . 

Single-phase 

Edison  three-wire,  d. 

section 

Edison   three-wire,   d. 

section 

Inverted  three-phase  (derived  from  two  branches  of  a 
-3-phase  system  by  transformation  by  means  of  two 

transformers,  whose  secondaries  are  connected  in 

opposite  direction  with  respect  to  their  primaries) . . . 

Quarter-phase  with  common  return 

Three-phase 

Three-phase  with  neutral  wire,  full  section 

Three-phase  with  neutral  wire,  half  section 

Independent  quarter-phase 

Edison  five-wire,  d.  c.  or  single-phase,  full  neutral 

Edison  five-wire  d.  c.  or  single  phase,  half  neutral 

Four  wire,  quarter  phase,  with  common  neutral,  full 

section 

Four  wire,  quarter-phase,  with  common  neutral,  half 

section.  . 


TOO 
100 

37-5 
31-25 


56-25 
72-9 
75-o 
33-3 
29.17 
100 

i5-625 
10.93 

31-25 
28.125 


106 


ELECTRIC   POWER  CONDUCTORS 


We  see  herefrom  that  in  distribution  for  light- 
ing, with  the  same  minimum  potential  and  with 
the  same  number  of  wires,  the  single  phase  system 
is  superior  to  any  polyphase  system. 

COMPARISON    OF   SYSTEMS   WITH   EQUAL   MAXIMUM 
POTENTIAL  TO  GROUND 


No. 

of 

Wires 


System. 


Relative 

Amount  of 

Copper. 


Single-phase,  either  without  ground  *  or  with  one  wire 

ground  ed 

Single-phase,  center  grounded 

Continuous  current,  either  without  ground*  or  with 

one  wire  grounded , 

Continuous  current,  center  grounded 

Three-phase,  either  without  ground*  or  with  one  wire 

grounded , 

Three-phase,  neutral  grounded 

Quarter-phase  with  common  return,  without  ground  or 

with  either  outer  grounded 

Quarter-phase  with  grounded  common  return 

Independent  quarter-phase,  either  without  ground  *  or 

with  one  wire  grounded 


100 

25 


I2-5 

75 
25 

M5-7 
72.9 


*  Even  when  no  part  of  the  system  is  grounded  each  wire  has  to  be  insulated 
from  ground  for  a  difference  of  potential  equal  to  that  between  wires,  since  the 
difference  of  potential  between  any  wire  and  ground  rnay  be  anything  from  zero 
to  full  potential  between  wires. 

Since  the  comparison  is  made  on  the  basis  of 
equal  maximum  potential  and  the  maximum  poten- 
tial of  an  alternating  system  is  V2  times  that  of  a  con- 
tinuous-current circuit  of  equal  effective  potential, 
the  alternating  circuit  of  effective  potential  e  com- 
pares with  the  continuous-current  circuit  of  potential 
eV2,  which  latter  requires  only  half  the  copper  of 
the  alternating  system. 

(The    author    is    indebted    to    C.    P.    Steinmetz, 


DETERMINATION  OF  SIZE  OF  CONDUCTORS    107 

"  Alternating    Current    Phenomena,"   for    much    of 
the  above  data.) 

Standard  Transmission  Line  Voltages.  The  following 
three-phase  voltages  have  been  adopted  by  the  Gen- 
eral Electric  Company  as  standard  for  railway  work: 

11,000  volts  with  delta  connected  transformers. 

19,000  volts  with  delta  connected  transformers. 

33,000  volts  "  Y  "  or  delta  connected  transformers. 

57,000  volts  "  Y  "  connected  transformers. 
These  voltages  step  up  in  the  ratio  of  the  square 
root  of  three  to  one,  allowing  the  voltage  of  any 
system  to  be  raised  in  case  of  extensions  from  one 
standard  to  the  next  higher,  by  changing  the 
transformer  primary  connections  from  delta  to  "  Y." 
The  lowest  voltage  (11,000),  is  the  only  one  suited 
for  direct  generation  without  step-up  transformers, 
and  is  generally  so  installed.  Such  systems  are 
not  readily  changed  over,  for  which  reason  19,100 
volt  transformers  are  delta  connected  only.  On 
account  of  the  prevailing  use  of  13,200  volts,  trans- 
formers and  switching  apparatus  can  be  supplied 
for  this  voltage  also.  (G.  E.  Review,  May,  1908.) 

2.   LAMP  WIRING  CALCULATIONS 
PRELIMINARY 

THE  following  data  are  necessary  for  the  wiring 
calculations. 

(i)  Length  of  feeder  from  bus  to  branches.  Use 
length  of  wire,  which  is  usually  twice  the  distance. 


108 


ELECTRIC  POWER  CONDUCTORS 


(2)  Number  of  branches. 

(3)  Length    of    wire    and    current    taken    by    each 
branch. 

(4)  Permissible  volts  drop  from  bus  to  branches, 
in  both  wires. 

(5)  Permissible  volts  drop  in  each  branch.     Usually 
the  same  for  all  branches. 

Calculation  of  Wire  for  Branches.  Construct  a 
table  as  shown  below,  giving  for  each  branch  the 
permissible  drop,  the  length  of  wire,  and  the  current. 


Then  by  the  formula  C.M.  = 


10 . 8  X  ampere-feet 
Volts  drop 


,  the 


size  of  the  wire  is  calculated. 

TABLE  FOR  CALCULATION  OF  BRANCH  WIRES 


Branch 
Number. 

Permissible 
Drop  of 
Volts  in 
Branch  =  v. 

Length  of 
Wire  in 
Branch. 
Feet  =  F. 

Amperes 
taken  by 
Branch  =  .<4. 

io.8AF_ 

V 

Circular  Mils. 

Size 
B.  &  S 

I 

2 

3 

etc. 

Calculation  of  Wire  for  Feeder  or  Main. 

i  o .  8  X  total  current  X  total  length 
Permissible  volts  drop 

While  the  above  form  is  the  most  usual,  the  formula 
may  also  be  written  as  follows: 

1080  X  total  ampere-feet 


C.M. 


pXV. 


DETERMINATION  OF  SIZE  OF  CONDUCTORS    109 


where    V  =  volts  delivered, 

p  =  drop  in  mains  in  per  cent  of  volts  delivered. 

Slide  Rule  for  Wiring.  A  simple  slide  rule  for 
wiring  calculations  devised  by  E.  P.  Roberts,  is 
made  by  constructing  a  table  as  shown  below,  and 
cutting  along  the  line  between  the  first  and  second 
columns. 


Size  of  Wire. 

Thousands  of 
Ampere  Feet. 
Thousands  of 
Circular  Mils. 
Volts  Loss. 

500 

500 

400 

400 

320 

320 

250 

250 

0000 

2OO 

ooo 

1  60 

oo 

I25 

o 

IOO 

I 

80 

2 

64 

3 

50 

4 

40 

5 
6 

32 
25 

7 
8 

20 

16 

9 

12 

10—  > 

IO 

ii 

8 

12 

6 

13 

5 

14 

4 

15 

16 

3 

2 

17 

2 

110  ELECTRIC  POWER  CONDUCTORS 

Then  to  use  the  rule  all  that  is  required  is  to  put 
the  arrow-head  opposite  the  figures  in  the  second 
column  representing  volts  loss  allowable,  and  oppo- 
site thousands  of  ampere-feet,  read  in  the  second 
column,  will  be  found  in  the  first  column  the  size  of 
the  wire  required. 

The  action  of  the  rule  is  based  upon  the  fact  that 
No.  10  wire  has  a  resistance  of  practically  one  ohm 
per  1000  feet,  and  therefore  with  No.  10  wire  10,000 
ampere-feet  would  give  10  volts  loss.  Also  No.  10 
wire  has  practically  10,000  circular  mils  cross-section, 
and  the  size  of  the  wire  doubles  for  each  third  size 
larger. 

Three- Wire  System.  The  outside  wires  are  calcu- 
lated by  the  above  rules,  ignoring  the  center  or 
neutral  wire,  and  treating  two  lamps  in  series  as 
one  lamp  of  double  voltage. 

The  neutral  wire  of  a  branch  is  usually  made  the 
same  size  as  the  outers,  although  in  most  cases  a 
smaller  size  would  be  possible. 

Alternating  Currents.  The  inductance  of  house 
wiring,  where  the  two  wires  of  a  circuit  are  run  in 
the  same  pipe  or  moulding,  is  negligible. 


I 
DETERMINATION  OF  SIZE  OF  CONDUCTORS   111 


3.    CONTINUOUS-CURRENT  RAILWAY  FEEDER 
CALCULATIONS 

PERMISSIBLE  POTENTIAL  DROP 

The  total  drop  of  potential  in  the  positive  and 
negative  conductors  is  governed  by  four  conditions, 
namely:  the  possibility  of  starting  the  cars,  the 
brilliancy  of  the  lights,  the  limiting  of  drop  in  the 
grounded  conductors  and  the  relative  economy  of 
low  first  cost  compared  with  low  energy  loss.  With 
regard  to  the  question  of  starting  the  cars,  the  voltage 
required  may  be  derived  from  a  study  of  the  motor 
curves. 

With  the  multiple-unit  system  of  control,  the  limit- 
ing voltage  is  usually  that  at  which  the  contactors 
will  operate  satisfactorily,  this  being  about  one-half 
the  normal  running  voltage.  The  voltage  at  which 
the  car  lights  become  too  dim  is  about  90%  of  the 
rated  voltage  of  the  group  of  lamps.  However,  by 
using  lamps,  rated  considerably  below  the  normal 
bus  voltage,  it  is^  permissible  to  let  the  voltage  drop 
more  than  10%  without  affecting  the  lights  too 
seriously;  although  lamps  thus  used  get  an  over- 
voltage  when  the  load  is  light,  causing  a  shortening 
of  their  life. 

The  drop  in  grounded  conductors  is  usually  covered 
by  city  ordinances,  which  require  it  not  to  exceed  a 
specified  amount. 


112  ELECTRIC  POWER  CONDUCTORS 

The  investment  in  a  system  of  conductors  may  be 
expressed  as  an  initial  cost  or  as  an  annual  interest 
thereon.  The  value  of  the  kilowatt-hours  of  energy 
lost  in  these  conductors  is  most  conveniently  expressed 
as  an  annual  expense.  The  sum  of  these  two  annual 
items  is  the  total  annual  expense  of  the  feeders, 
which  it  is  desirable  to  make  as  small  as  possible. 

AUXILIARY  FEEDERS 

Any  direct-current  feeder  system  consists  of  two 
distinct  parts,  the  conductors  which  supply  current 
from  the  power-house  to  the  line  and  the  contact 
conductors  which  yield  their  current  directly  to  the 
cars.  In  many  cases  the  contact  conductors  will  be 
sufficiently  large  to  fulfil  both  functions,  but  more 
often  they  are  supplemented  by  auxiliary  copper 
feeders.  The  various  steps  at  which  auxiliary  copper 
may  have  to  be  added  are  given  below  in  the  order 
in  which  they  usually  have  to  be  treated. 

I.  If  the  drop  in  the  grounded  conductors  exceeds 
the  legal  limit  or  the  limit  prescribed  by  danger  of 
electrolysis,  copper  will  have  to  be  added  to  these 
conductors. 

II.  If  with  this  additional  copper  the  total  drop 
in  the  positive  and  negative  feeders  is  still  too  great 
to  enable  the  cars  to  start,  additional  copper  must 
again  be  resorted  to,  but  this  time  it  may  be  added 
to  either  the  positive  or  negative  system.     Whether 
it  will  be  more  economical  to  add  it  to  the  positives 


I 

DETERMINATION  OF  SIZE  OF  CONDUCTORS   113 

or  negatives  will  have  to  be  worked  out  for  each  case, 
although  an  indication  is  given  by  the  fact  that  if 
the  unit  price  of  conductors  installed  is  the  same  for 
both,  it  is  more  economical  to  distribute  the  copper 
so  as  to  make  the  resistance  of  the  two  systems  equal. 

III.  Having  provided  copper  to  maintain  the  voltage 
high  enough  to  start  the  cars,  it  remains  to  deter- 
mine whether  it  is  also  high  enough  to  keep  the  lamps 
bright.     If  not,  more  copper  must  be  added  in  the 
way  described  above. 

IV.  The  feeder  system  having  been  made  of  ample 
dimensions  to  meet  all  the  conditions  of  the  service 
it  remains  to  determine  whether  the  annual  loss  in 
the  conductors  is  great  enough  to  justify  the  addition 
of  more  copper  in  order  to  keep  down  the  operating 
expenses.     If  the  conductivity  is  sufficient,   there  is 
nothing   to   be   done;     but   if   the   considerations   of 
operating  economy  call  for  more  copper,  the  engineer 
is  justified  in  recommending  it. 

In  order  to  determine  the  most  economical  copper 
investment,  it  is  convenient  to  compile  a  table  show- 
ing the  following  six  quantities:  (i)  Value  of  pro- 
posed additional  conductors.  (2)  Total  annual  energy 
loss  (kilowatt-hours)  in  the  entire  positive  and  nega- 
tive system,  including  the  proposed  additional  con- 
ductors. (3)  Value  of  this  lost  energy.  (4)  Value 
of  the  additional  conductors.  (5)  Annual  interest 
on  value  of  additional  conductors.  (6)  Sum  of  value 
of  total  annual  energy  loss  and  the  interest  on  pro- 


114  ELECTRIC  POWER  CONDUCTORS 

posed  additional  conductors.  When  selecting  the 
figures  for  the  first  column  two  values  should  be 
assumed  initially  and  all  the  other  columns  worked 
out  for  them,  in  order  to  give  an  indication  of  the 
range  of  values  which  is  most  convenient  to  work 
with. 

An  abbreviation  of  this  calculation  is  given  under 
Kapp's  and  Fender's  modifications  of  Kelvin's  law.  , 

V.  If  after  these  conditions  are  satisfied,  the  carry- 
ing capacity  is  insufficient,  more  copper  must  be 
added. 

DISTRIBUTION  OF  CURRENT 

A  certain  current  passing  from  the  positive  to  the 
negative  system  at  the  end  of  the  line  farthest  from 
the  power  station  being  assumed  to  cause  a  total 
drop  of  V  volts,  the  same  total  current  taken  from 
from  the  line  in  n  equal  amounts  at  n  equidistant 
points  along  the  line  will  produce  a  total  drop  of 

(i+  — )  —  volts.     If   n  is  infinite,  that  is,  if  the  drain 
n]  2 

of  current  is   uniform  along   the  line,  the   drop    will 

y 

be  — .     If,  however,  n  is  not  infinite,  the  drop  will 
2 

be  greater  than  —  by  -  -  per  cent,  a  quantity  which  is 

quite  small  when  n  is  considerable.  It  is  therefore 
usual  to  assume  a  uniform  drain  of  current,  a  procedure 


* 
DETERMINATION  OF  SIZE  OF  CONDUCTORS    115 

which  is  further  justified  by  the  continuous  motion  of 
the  load  which  causes  it  to  act  as  if  more  distributed. 
Such  an  assumption,  however,  is  by  no  means 
justifiable  on  interurban  or  trunk  line  railroads,  as 
in  such  cases  the  trains  are  usually  far  apart.  This 
case  is  treated  separately  below. 

DISTRIBUTION  OF  COPPER 

The  drop  of  potential  depends  largely  on  how 
the  copper  is  distributed  along  the  line.  It  is  there- 
fore important  to  secure  the  most  economical  dis- 
tribution of  copper  which  will  give  the  required 
drop.  The  auxiliary  copper  may  be  connected 
to  the  contact  conductor  at  such  frequent  inter- 
vals that  it  virtually  forms  a  part  of  it;  it  may, 
on  the  other  hand,  be  connected  at  one  end  only, 
or  it  may  be  connected  at  such  distances  as  not  to 
be  covered  by  either  of  the  above  cases.  Each  of 
these  schemes  requires  separate  consideration,  a 
general  method  of  treatment  being  given  for  each, 
which  covers  the  addition  of  copper  to  either  the 
positive  or  negative  system,  as  the  case  may  require. 

AUXILIARY  COPPER  FREQUENTLY  CONNECTED 

The  diagram  in  Fig.  13  shows  the  most  economical 
way  of  distributing  the  feeder  metal;  the  formulas  for 
circular  mils,  volume  of  copper,  watts  lost  and 


116 


ELECTRIC  POWER  CONDUCTORS 


potential  drop  are  also  given.*     The  following  symbols 
are  used  in  both  Figs.  13  and  14. 

C.M.  =Area  in  Circular  mils,  where  one  C.M.  is  the 
area  of  a  circle  of  Viooo  inch  diameter. 


FIG.  13. 

C.M. -Ft.  =  Volume  in  Circular  mil-feet,  where  one 
C.M. -Ft.  is  the  volume  of  a  cylinder  of  one  c.m.  area 
and  one  foot  long.  A  volume  of  copper  in  c.m. -ft. 
divided  by  any  number  of  c.m.  gives  the  number 
of  feet  of  cable  of  that  area  required  to  make  up  the 
given  volume  of  copper. 


FIG.  14. 

r=the  resistance  of  a  c.m.-ft.  of  copper,  measured 
along  its  length,  at  about  60°  F. 
r  =  10.2  for  copper  of  100%  cond 

10.3  for  copper  of  99%  cond. 

10.4  for  copper  of  98%  cond. 

10.5  for  copper  of  97%  cond. 

*  See  Appendix  4. 


* 
DETERMINATION  OF  SIZE  OF  CONDUCTORS    117 

If  the  conductors  are  partly  of  iron,  as  with  a 
third  rail,  it  is  usual  to  reduce  the  area  of  iron  to  its 
equivalent  area  of  copper. 

F=drop  of  potential  from  the  station  bus  to  the 
end  of  the  line  in  either  the  positive  or  negative 
conductors,  as  the  case  may  be. 

A  =  total  current  delivered  from  the  station  bus 
to  the  section  under  consideration. 

L=  length  of  the  section,  feet. 

00=  distance  (feet)  of  any  point  from  the  end  of 
the  line  farthest  from  the  station. 


V 


Drop  =  —  -=  •  x/*3, 
\/L3 


Watts  lost  = 
5 


It  is,  of  course,  impossible  to  exactly  realize  the 
most  economical  distribution  in  practice,  so  that 
a  series  of  steps,  as  shown  in  the  second  diagram, 
should  be  arranged  so  as  to  approximate  as  closely 
as  possible  to  the  theoretical  curve.  It  should  be 
remembered  that  the  curve  of  most  economical  dis- 


118  ELECTRIC  POWER  CONDUCTORS 

tribution    shows    the    total    feeder    metal,    including 
the  contact  conductors. 

The  approximation  to  the  most  economical  dis- 
tribution is  calculated  in  the  following  way.  Refer- 
ring to  Fig.  14: 

X\  =  distance  ED,  and  Y\  =c.m.  01  copper  in  ED. 
X2  =  distance  EC,  and  Y2  =c.m.  of  copper  in  DC. 
X%  ==-- distance  EB,  and  Y%  =c.m.  of  copper  in  CB. 
X*  =  distance  EA,  and  F4  =c.m.  of  copper  in  BA. 


Drop  in  DE  =k- 


"       AB=k' 


4       ^v   3 


Y* 

Total  watts  lost  - 


DETERMINATION  OF  SIZE  OF  CONDUCTORS    119 

The  drop  given  by  the  above  formula  is  from  the 
far  end  of  the  line.  The  drop  from  the  station  end 
may  be  obtained  by  subracting  this  value  from  V. 


AUXILIARY  COPPER  CONNECTED  AT  END 

The  auxiliary  feeder,  in  this  case  being  merely  a 
uniform  conductor  with  the  same  current  along  its 
entire  length,  may  be  treated  by  Ohm's  law  in  its 
simplest  form.  Auxiliary  conductors  of  this  sort  are 
useful  in  connection  with  grounded  retjrns  in  which 
it  is  desired  to  minimize  the  drop.  Two  or  more 
insulated  conductors,  connected  to  the  line  at  various 
points  will  each  take  off  its  proportion  of  the  current 
without  making  the  entire  current  accumulate  near 
the  station,  as  would  be  the  case  with  a  single  con- 
nection direct  from  the  bus.  This  gives  rise  to  a  series 
of  rises  and  falls  of  potential  along  the  line,  but  there 
will  be  no  serious  drop  in  the  grounded  conductors, 
irrespective  of  what  the  drop  may  be  in  the  insulated 
feeders  connected  thereto. 


FEEDERS  INFREQUENTLY  CONNECTED 

This  condition  occurs  where  a  feeder  cable  runs 
parallel  to  the  line  and  is  tapped  in  at  intervals 
through  circuit  breakers  or  switches.  The  expense 
of  the  breakers  renders  it  necessary  to  have  as  few 
such  connections  as  possible.  Fig.  15  shows  an 


120 


ELECTRIC  POWER  CONDUCTORS 


example  of  such  a  system,  comprising  four  conduc- 
tors, some  of  which  may  be  contact  conductors  and 
others,  auxiliary  feeders.  Fig.  16  shows  this  scheme 


Positive  Contact  Conductors 
C  D 


c 

D 

c 

D 

A         |    E 
^Generator                    LoadQ) 

H           |G 

3 
Generator^ 

H 
Ti#ck  Kails 

FIG.  15. 

in    diagrammatic    form    with    corresponding    points 
indicated  by  identical  letters. 

The  resistance  of  this  system  may  be  calculated  in 


two  ways,  the  first  of  which  is  simpler,  but  the  second 
more  complete,  as  it  gives  the  point  of  maximum 
resistance. 


DETERMINATION  OF  SIZE  OF  CONDUCTORS  121 


First  Method.  Referring  to  Figs.  15  and  16,  the 
resistances  of  the  various  sections  are  designated  as 
follows  : 


Points. 

Conductors. 

Resistance. 

Ej  to  A 

All  tracks 

C 

E2to  B 

All  tracks 

d 

CtoD 

All  feeders  but  one 

e 

A  to  L 

One  track 

a 

B  to  L 

One  track 

b 

Fl  to  G 

All  tracks* 

m 

F2  to  G 

All  tracks* 

n 

*  Including  negative  feeders. 

Resistance  from  load  to  both  substations  equals 
AF- 


B 


where 


A  +  F- 
A  = 


(Derivation  of  above  formula  given  in  Appendix  IV.) 
Second  Method.     Where  the  maximum  resistance  is 
required,  the  following  formulas  may  be  used.     The 
resistances  and  lengths  are  as  follows: 

R  =  resistance  of  third  rail  per  1000  ft.; 
r  =  resistance  of  all  track  rails  per  1000  ft. 
/  =  length  A  B  in  thousands  of  feet; 
x  =  distance  from  A  to  point  of  maximum  resistance, 
thousands  of  feet; 


122  ELECTRIC  POWER  CONDUCTORS 

c=  resistance  from  EI  to  A,  all  tracks; 
d  =  resistance  from  E2  to  B,  all  tracks; 
k  =  resistance  from  FL  to  H  ,  all  tracks  ; 
y  =  resistance  from  F%  to  I,  all  tracks  ; 


,  say; 


*">+' 


Then 

^   ,^ 

Resistance 


and  resistance  is  a  maximum  where 


(Derivation  of  above  formula  given  in  Appendix 
IV.) 

Third  Method.  Unlike  the  two  previous  methods, 
this  is  intended  to  be  used  where  there  is  only  one 
substation  feeding  the  section,  as  shown  in  Fig.  17. 


I 
DETERMINATION  OF  SIZE  OF  CONDUCTORS   123 

Let  R  =  resistance   in   ohms   per   thousand   feet   of 

single  contact  conductor; 
r  =  resistance   in   ohms   per   thousand   feet   of 

combined  track  rails; 
e  =  multiple  resistance  of  all  conductors  between 

A  and  B  except  the  loaded  one; 


M+*' 


Auxiliary  Feeders 


Contact  Conductors 

h  -x  
L^  /,,..._       *- 

i 

(Only  Positives  Shown) 

FIG.  17. 
D  =  resistance  from   b  to   c.    all   conductors   in 

multiple ; 

E  =  r X length  be  in  thousands  of  feet; 
x  =  distance  from  b  to  point  of  maximum  re- 
sistance from  substation; 
^4 

=  28' 

The  resistance  from  substation  to  ooint  of  maxi- 
mum resistance  from  substation, 


124 


ELECTRIC   POWER  CONDUCTORS 


This  may  be  applied  to  the  section  be  as  well  as  to 
the  section  ab. 

Fourth  Method.  The  circuit,  shown  in  Fig.  18,  is 
that  of  a  feeder  system  in  which  both  positive  and 
negative  feeders  are  infrequently  cross-bonded. 


.Substation 


li 

FIG.  1  8. 


O  Substation 


The  resistances   are   designated   by  letters   on   the 
diagram  and  by  the  following: 


DETERMINATION  OF  SIZE  OF  CONDUCTORS    125 

The  total  resistance  from  the  load  to  both  sub- 
stations in  multiple  is  given  by  the  following  expres- 
sion: 


DB 


(The  derivation  of  the  above  formula  is  given  in 
Appendix  IV.) 

If  there  are  several  trains  between  the  two  sub- 
stations, the  maximum  drop  in  the  section  will  be  the 
sum  of  the  drops  computed  for  each  train  as  if  it 
were  the  only  one  on  the  line,  and  the  trains  should 
be  distributed  so  as  to  give  the  worst  condition 
that  would  arise  in  practice. 

MISCELLANEOUS  FORMULAE 

The  potential  drop  in  any  uniform  conductor  in 
which  the  current  varies  along  its  length,  is  given  by 

Volts  =  ohms   per  ft.  X  area   of   current   curve   in 
ampere-feet. 

The  \vatts  lost  in  any  conductor  along  which  there 
is  a  uniform  drain  of  current  are  given  by 

Watts  lost  =  amperes  per  ft.  X  area  of  drop  curve 
in  volt-feet. 

If  a  curve  of  potential  drop  in  any  feeder  system 
be  plotted  for  one  load,  the  drop  curve  for  any  other 


126 


ELECTRIC  POWER  CONDUCTORS 


load  similarly  distributed  may  be  derived  from  it  by 
merely  changing  the  ordinates  in  the  ratio  of  the  two 
loads  in  question. 

VALUE  OF  CURRENT  USED  IN  CALCULATIONS 


Purpose. 

Current. 

Electrolysis. 

Depends  upon  local  ordinances. 

Car  starting  

Average  current  during  half  minute  of  maximum  load. 

Car  lighting? 

If  cars  are  closely  spaced,  the  R.M.S.  current  during 

hour  of  maximum  load.  If  cart  are  infrequent,  it 
is  better  to  use  various  unit  train  loads  and  esti- 
mate whether  their  effect  upon  the  candle-power 
is  excessive,  when  concentrated  at  various  points. 

Copper  economy..  - 

R.M.S.  current  of  whole  year.  If  the  trains  are  too 
infrequent  to  permit  the  assumption  of  uniform 
current  drain,  the  best  approximation  is  to  assume 
the  R.M.S.  current  for  the  year,  concentrated  at 
the  point  of  average  resistance. 

Heating  of  cables.. 

R.M.S.  current  taken  over  several  periods  of  maxi- 
mum load. 

Let  ii,  1*2,  fc',3,  etc.,  be  the  currents  flowing  for  t\,  1%, 
t3,  etc.,  minutes  respectively,  and  let  -T  be  the  minutes 
in  the  total  interval  considered.  Then  the  R.M.S.  cur- 


rent = 


UNIVERSITY 


( -- 


DETERMINATION  OF  SIZE  OF  CONDUCTORS    127 


COST  OF  ENERGY 

The  cost  of  producing  energy  may  be  divided  into 
two  items. 

Fixed  Charges,  which  are  independent  of  varia- 
tions of  output,  and 

Operating  Expenses,  which  are  practically  propor- 
tional to  the  output.  Fuel,  water,  and  oil  are 
included  in  this  item. 

In  feeder  calculations  only  the  operating  expenses 
should  be  used  because  the  fixed  charges  exist  inde- 
pendent of  any  saving  in  line  losses. 

4.    NEGATIVE  BOOSTER  CALCULATIONS 

IN  railway  feeder  work  it  is  usual  to  assume  the 
load  to  be  uniformly  distributed  along  the  line,  so 
that  going  towards  the  power  station  the  current 

+  550, ±25 ±500 

ifl, 

1 4-10  +20 


JJ 


R  0 

FIG.  19. 

in  the  negative  feeders,  including  the  return  rails, 
uniformly  increases.  The  current  flowing  in  the  feed- 
ers to  the  bus  bars  will  then  be  represented  by  a 
straight  line  diagram,  provided  that  all  the  feeders 
are  connected  together  so  as  to  virtually  form  one 
conductor.  When,  however,  a  booster  cable  is  con- 
nected to  the  negative  feeders,  as  shown  in  Fig.  19, 


128 


ELECTRIC   POWER  CONDUCTORS 


the  booster  cable  being  insulated  from  the  other 
feeders,  except  at  one  point,  the  current  will  be 
drawn  from  the  line  into  the  booster  cables  and  the 
current  diagram  will  take  one  of  the  forms  shown  in 


FIG.  20. 

Fig.  20,  these  four  forms,  however,  being  treated  in 
exactly  the  same  way  in  the  voltage  calculations  de- 
scribed below.  Case  I  shows  a  booster  which  entirely 
neutralizes  the  drop  in  the  booster  cables  and  re- 
.duces  the  point  of  connection,  /,  to  the  same  po- 
tential as  the  bus  bar.  In  this  case  current  is  drawn 


DETERMINATION  OF  SIZE  OF  CONDUCTORS     129 

into  the  booster  tables  from  both  sides  of  the  point  of 
connection,  the  current  dividing  at  a  point  /,  from 
which  the  resistance  to  the  bus  equals  the  resistance 
to  the  point  /.  In  Case  II,  the  booster  only  par- 
tially neutralizes  the  drop  in  its  cables,  but  draws 
current  from  both  sides  of  the  point  of  connec- 
tion. Case  III  shows  a  booster  drawing  current  only 
from  beyond  the  point  of  connection,  the  whole  of  the 
current  on  the  other  side  returning  to  the  bus  by  the 
line  feeders.  In  Case  IV,  the  booster  draws  only  part 
of  the  current  from  beyond  the  point  of  connection, 
the  remainder  returning  to  the  bus  through  the 
line  feeders  with  the  current  from  between  the 
station  and  that  point.  A  fifth  case  might  be  added 
to  these,  which  is  only  useful  when  the  permissible 
drop  is  very  small.  In  this  case  the  point  of  con- 
nection, 7,  is  maintained  at  a  lower  potential  than 
the  negative  bus  itself. 

The  relation  between  line  drop,  booster  E.M.F. 
and  current  may  be  found  either  by  calculation  or 
graphically.  Considering  the  former  method  first, 
let 

a  =  amperes  entering  negative  feeder  system  per  foot 
of  line; 

r  =  resistance  of  negative  feeder  system  per  foot ; 

i  =  total  amperes  entering  negative  feeder  system ; 

io  =  total  amperes  taken  off  by  booster ; 

l=HI  =          =  distance  from  H  to  the  point  at  which 


130  ELECTRIC  POWER  CONDUCTORS 

the    current  in  the  negative  feeders  is  zero.      (Fig. 

21); 

t^'JD. 

The  volts  drop  in  the  various  sections  of  the  negative 
feeder  is 

From  Htol:     D 
/to/:  Dl- 
JtoD:    D2 


FIG.  21. 


These   drops   can   be   read   directly   from   a   curve 
plotted  from  the  equation 


The  drop  to  the  point  /  is  (D  —  Di)  and  the  total 
drop  is  (D-Di  +  D2). 
The  booster  voltage  is 


where  R  is  the  resistance  of  the  booster  cable. 

In  case  /o  <  |/  the  current  curve  takes  the  form 
shown  in  Case  IV,  Fig.  20. 


* 
DETERMINATION  OF  SIZE  OF  CONDUCTORS    131 

In  this  case  there  is  no  point  in  the  negative  feeders 
at  which  the  current  is  zero.  Mathematically,  how- 
ever, we  still  define  the  distance  HI  by  the  formula 

e-   — .     The  length  /i  is  then  negative,  but  since  the 

lengths  are  squared  in  the  above  formula  for  drop, 
these  formulas  also  hold  in  this  case. 


N 


FIG.  22. 


The  voltage  curves  shown  in  Figs.  20  and  22  are 
composed  of  parts  of  a  general  voltage  curve,  the 
equation  of  which  is 


where 

V=  voltage  rise  from  where  the  current  is  zero,  to 
a  point  D  feet  away. 

a  =  current  increment  in  amperes  per  foot,  i.e., 
total  load  on  section  divided  by  length  of  section. 

r=  resistance  of  return  conductors  per  foot  of 
line. 

Therefore,  if  one  such  curve  be  drawn  with  its 
corresponding  current  diagram  over  it,  as  shown  in 
Fig.  23,  the  voltage  curve  for  any  of  the  schemes 
shown  in  Fig.  20  may  be  traced  from  it. 


132 


ELECTRIC  POWER  CONDUCTORS 


Thus  to  obtain  the  voltage  curve  shown  in  Fig.  22, 
set  off  HD  and  DP  on  tracing  paper  to  the  same 
scale  as  the  general  voltage  curve,  and  select  any 
point  ]  for  the  booster  feed  point.  Put  P  over 
the  point  0  on  the  general  curve,  make  HD  parallel 
to  XX,  and  trace  the  voltage  curve  to  M,  where 
it  intersects  the  perpendicular  through  /.  Then, 
still  keeping  HD  parallel  to  XX,  run  M  along  the 
general  voltage  curve  until  H  lies  on  that  curve. 


The  intersection  of  OF  and  HD  is  the  point  7  where 
the  current  divides.  This,  having  been  marked,  avoid 
shifting  the  papers  and  trace  the  remainder  of  the 
voltage  curve,  i.e.,  HNM. 

Knowing  I,  draw  the  current  diagrams  HGI  and 
JKI  (Fig.  21).  The  current  in  the  booster  and  its 
cable,  will  be  the  sum  of  JK  and  JC.  The  booster 
voltage  will  be  the  sum  of  the  drop  in  the  booster 
cables,  and  (DP-MP),  Fig.  22.  This  should  be 
tried  for  various  positions  of  /,  and  the  best  selected. 


DETERMINATION  OF  SIZE  OF  CONDUCTORS   133 

5.   ALTERNATING-CURRENT  TRANSMISSION  LINE 
CALCULATIONS  * 

(From  an  article  by  H.  Fender,  also  published  in  part  in  the  Electrical 

World.} 

Let  E=  pressure  between  adjacent  wires  at  receiv- 
ing end  in  kilovolts  (thousands  of  volts) ; 
V  =  pressure  between  adjacent  wires  at  the  gen- 
erating end  in  kilovolts    (thousands   of 
volts) ; 
W  =  power  delivered  in  megawatts   (thousands 

of  kilowatts) ; 
k=  power  factor  of  the  load  expressed  as  a 

decimal  fraction; 
/  =  tangent  corresponding  to  k=cosa   (Table 

Hi); 

^o=  power  factor  at  the  generating  end,  ex- 
pressed as  a  decimal  fraction; 

L  =in  case  of  a  three-phase  system,  the  length 
of  each  wire  in  miles;  in  the  case  of  a 
single-phase  system,  the  total  length  of 
both  wires  in  miles; 

r  =  resistance  of  each  conductor  per  mile; 
x  =x1+x2=  reactance  of  each  conductor  per 
mile,  where  %\  is  the  reactance  per  mile 
of  a  number  oooo  B.  and  S.  wire  (Table  I), 
and  #2  the  difference  in  the  reactance 
per  mile  of  a  No.  oooo  wire  and  that  of 
the  wire  actually  used  (Table  II) ; 

*  See  Appendix  IV  for  derivation  of  formulae. 


134 


ELECTRIC  POWER  CONDUCTORS 


Q  =  power  lost  in  transmission  as  a  fraction  of 

the  delivered  power; 
P  =  pressure  drop  as  a  fraction  of  the  delivered 

pressure. 

(kE)2 
R  =  —         =  equivalent    resistance    of    receiver 


per  mile  of  line* 


TABLE  I 

REACTANCE  PER  MILE  OF  A  No.  oooo  B. 


S. 


Distance  Apart 
of  Wires  in 
Feet. 

15  Cycles. 

25  Cycles. 

40  Cycles. 

60  Cycles. 

125  Cycles 

I 
2 

3 

0.128 
0.149 
0.161 

0.213 
0.248 
0.268 

0.340 
0.396 
0.429 

0.510 

0-594 
0.644 

1.063 
1.238 
I-34I 

4 
5 
6 

0.170 
o.  176 
0.182 

0.283 
0.294 
0.303 

0.452 
0.470 
0.485 

0.678 

0.705 
0.728 

!-4i3 
1.470 
1.516 

7 
8 

9 

0.187 
o.  191 
0.104 

0.311 
0.318 
0.324 

0.498 
0.508 
0.518 

0.746 
0.763 

o-777 

i-555 
1.589 
1.618 

10 

15 

20 

0.197 

0.210 

0.218 

0.329 

o-35^ 
0.364 

0.526 

o-559 

0.582 

0.790 
0.839 
0.874 

1.645 
1.748 
1.820 

25 

0.225 

0-375 

0.601 

0.901 

1.877 

Case    I.     Given    the    delivered    pressure    E,    the 
power  delivered  W,  the  power  factor  of  the  load  k, 


DETERMINATION  OF  SIZE  OF  CONDUCTORS   135 

the  length  of  the  line  L,  the  frequency,  the  size,  and 
spacing  of  the  wires.  The  following  are  exact  expres- 
sions *  for  the  quantities  to  be  determined. 

Y 

Powerless  Q=—. 

/v 

Pressure  drop  P  =  k V(i+Q)2  +  T2 - 1 . 

Power  factor  at  generating  end  k0  = j^k. 

Case  II.  Given  the  delivered  pressure  E,  the 
power  delivered  W,  the  power  factor  of  the  load  k, 
the  length  of  the  line  L,  the  frequency  and  the  allow- 
able power  loss  Q.  The  size  wire  to  use  is  determined 
by  the  following  exact  formula: 

Resistance  of  each  wire  per  mile,  r=RQ, 

the  corresponding  size  of  wire  being  given  in  Table  II. 
The  pressure  drop  and  power  factor  at  the  generat- 
ing end  can  then  be  determined  by  the  formulae 
given  in  Case  I. 

Case  III.  Given  the  delivered  pressure  E,  the 
power  delivered  W,  the  power  factor  of  the  load  k, 
the  length  of  the  line  L,  the  frequency  and  spacing 
of  the  wires,  and  the  allowable  pressure  drop  P. 

An  exact  determination  of  the  size  of  wire  to  use 
in  this  case  cannot  be  made  directly,  since  this  would 

*  These  formulae  can  also  be  used  to  determine  the  overall  efficiency, 
regulation  and  power  factor  of  any  number  of  circuits  in  series  (e.g.  line  and 
transformers)  if  we  let  r  and  x  represent  the  sum  of  the  component  resist- 
ances and  reactances  respectively  and  R  the  total  equivalent  resistance  of 
the  receiver. 


136  ELECTRIC  POWER  CONDUCTORS 

require  the  solution  of  a  logarithmic  equation. 
However,  since  the  reactance  of  commercial  sizes 
of  wire  for  a  given  frequency  and  spacing  differ  but 
slightly  from  one  another,  a  close  approximation 
to  the  exact  size  of  wire  to  use  can  be  obtained  by 
assuming  that  the  reactance,  for  a  given  frequency 
and  spacing,  for  any  size  between  1,000,000  circular 
mils  and  a  No.  6  B.  and  S.  wire  is  equal  to  that  of 
a  No.  oooo  wire.  It  will  be  found  that  except  when 
the  line  reactance  is  large  compared  to  the  line 
resistance,  the  error  due  to  this  assumption  will 
not  cause  a  change  in  the  size  of  wire;  that  is,  the 
error  will  be  less  than*  half  the  percentage  difference 
(26%)  between  successive  sizes  on  the  B.  and  S. 
gauge.  On  the  other  hand  a  large  error  in  the 
approximate  formula  for  the  size  of  wire,  indicates 
immediately  that  the  drop  is  due  chiefly  to  the 
line  reactance,  and  that  by  allowing  a  very  small 
increase  in  the  permissible  drop,  or  by  employing 
two  separate  circuits  instead  of  one,  a  very  consid- 
erable saving  in  copper  can  be  effected. 
Put 


where  %\  is  the  reactance  of  a  No.  oooo  wire.  Then  to 
a  close  approximation,  resistance  of  each  wire  per 
mile 


r\  = 


DETERMINATION  OF  SIZE  OF  CONDUCTORS   137 


the  corresponding  size  of  wire  being  given  in  Table  II, 
as  well  as  the  difference  x2  between  the  reactance 
corresponding  to  this  size  and  the  reactance  of  a 
No.  oooo  wire. 

TABLE  II 

RESISTANCE*  PER  MILE   OF   COPPER  AND   ALUMINUM 
CABLES   AND   REACTANCE   INCREMENT  x2. 


Size  C.M. 
and 
B.  &  S. 

Ohms  per  Mile  at  20°  C. 

Difference  in  Reactance  per  Mile  of  any  Size 
Wire  and  that  of  No.  oooo  B.  &  S.  Wire  =  *2.t 

Copper. 

Aluminum. 

15 
Cycles. 

25 
Cycles. 

40 
Cycles. 

60 
Cycles. 

125 
Cycles. 

1,000,000 

0.0566 

0.0894 

—  0.024 

-0.039 

—  0.063 

-0.094 

-0.196 

900,000 

0.0629 

0.0993 

—  0.022 

-0.037 

-0.059 

-0.088 

-0.183 

800,000 

0.0707 

0.1118 

—  O.O2O 

-0.034 

-0.054 

-0.081 

-0.168 

700,000 

0.0808 

0.1278 

—  O.OlS 

-0.030 

—  0.048 

-0.073 

—  0.152 

6co,ooo 

0.0943 

0.1490 

—  0.016 

—  0.026 

—  0.042 

—  0.063 

—  0.132 

500,000 

0.1131 

0.1788 

—  0.013 

—  O.022 

-0.035 

—  0.052 

—  0.109 

450,000 

0.1257 

0.1987 

—  o.on 

—  O.OI9 

—  0.031 

—  0.046 

-0.095 

400,000 

0.1414 

0.224 

—  0.005 

—  O.OO9 

—  0.014 

—  O.O2I 

—  0.044 

350,000 

0.1616 

°-255 

—  0.008 

—  0.013 

—  O.O20 

—  0.031 

—  o  .  064 

300,000 

0.1886 

0.298 

-0.005 

—  0.009 

—  0.014 

—  0.021 

—  0.044 

250,000 

0.226 

o.358 

-0.003 

—  O.OO4 

—  O.007 

—  o.oio 

—  O.O2I 

oooo 

0.267 

0.423 

ooo 

0-337 

0-533 

+  0.004 

+  O.OO6 

+  O.OO9 

+  0.014 

+  O.O29 

00 

0.425 

0.672 

+  0.007 

+  O.OI2 

+  O.OI9 

+0.028 

+  0.059 

o 

o-536 

0.848 

+  O.OII 

+  0.018 

+  0.028 

+  0.042 

+  0.088 

I 

0.676 

i.  068 

+  0.014 

+  0.023 

+  0.038 

+  0.056 

+  o  117 

2 

0.852 

1-347 

+0.109 

+  0.029 

+  0.047 

+  0.070 

+  0.147 

4 

1-355 

2.14 

+  0.025 

+  0.041 

+  0.066 

+  0.098 

+  O.2O5 

6 

2-15 

3-4i 

+0.032 

+  0.053 

+  0.084 

+0.127 

+  0.264 

*  Stranded  wire,  copper  98%,  aluminum  62%  conductivity,  resistance  increased 
i%  on  account  of  stranding,  temperature  coefficient  0.42%  per  degree  C. 

t  The  total  reactance  of  a  wire  for  any  spacing  and  frequency  is  x  =  xi  +  xz  where 
xi  is  the  reactance  of  a  No.  oooo  wire  under  the  same  conditions. 


138  ELECTRIC  POWER  CONDUCTORS 

By    substituting    for    T\    in    the    above    formula 

the    value  T  =  T\+^-   the   error   in   the   value   of    r 
K 

caused  by  neglecting  x2  can  be  readily  found.  As 
stated  above,  in  any  practical  case  this  will,  as  a 
rule,  be  negligible,  but  should  the  error  in  the  par- 
ticular problem  in  hand  be  sufficient  to  give  a  new 
value  for  r,  for  which  the  corresponding  value  for 
%2  differs  appreciably  from  the  first  value  found,  r 
should  be  again  calculated,  using  this  second  value 
for  x2,  and  so  on,  until  the  difference  in  x2  for  two 
successive  values  of  r,  as  thus  determined,  becomes 
negligible.  In  this  w.ay  an  exact  determination  of 
the  size  corresponding  to  the  given  drop  can  be 
readily  made,  although,  as  stated  above,  a  large 
error  in  the  first  approximation  immediately  indi- 
cates that  the  feasibility  of  increasing  the  permis- 
sible drop,  or  of  dividing  the  circuit,  should  be 
investigated.  If  the  formula  gives  a  negative  value 
of  r,  it  is  impossible,  with  any  amount  of  copper,  to 
transmit  the  assumed  amount  of  power  with  the 
drop  and  inductance  assumed. 

Case  IV.  Given  the  pressure  at  the  generating 
end  V,  the  power  delivered  W,  the  power  factor  of 
the  load  k,  the  length  of  the  line  L,  the  frequency 
the  size  and  spacing  of  the  wires. 

In  this  case  R,  the  equivalent  resistance  of  the 
receiver  per  mile  of  line,  can  be  expressed  in  terms 
of  the  pressure  at  the  generating  end  V. 


•   * 


DETERMINATION  OF  SIZE  OF  CONDUCTORS  139 


Put 


Then 


M 


2LW 


M2 


Using  this  value  for  R,  the  exact  formulae  given  under 
Case  I  become  immediately  applicable. 

TABLE  III 

VALUES  OF  /=tan  CORRESPONDING  TO  £=cos  a 


k. 

o.oo. 

O.OI. 

O.O2. 

O.O3. 

O.O4. 

0.05. 

O.o6. 

0.07. 

0.08. 

0.09. 

o-5 
0.6 
0.7 

1.732 

1-333 
i.  020 

1.687 
1.299 
0.992 

1.643 
1.265 
0.964 

I.  600 
1-233 
0.936 

1-559 
I.  201 
0.909 

I.5I9 
1.169 
0.882 

1.479 
I.I38 
0.855 

1.442 
1.108 
0.829 

1.404 
1.078 
0.802 

1.368 
1.049 
0.776 

0.8 
0.9 

0.750 
0.489 

0.724 
0.456 

0.698 
O.426 

0.672 
0-395 

0.646 
0.363 

0.62O 
0.329 

0-593 
0.292 

0.567 
0.251 

0.540 
0.203 

0.512 
0.143 

Effect  of  Line  Capacity. — A  complete  and  accurate 
treatment  of  transmission  lines,  taking  into  account 
the  capacity  and  leakage,  is  given  below.  In  most 
practical  cases,  however,  the  leakage  is  negligible  and 
the  effect  of  line  capacity  can  be  determined  with 
sufficient  accuracy  by  assuming  that  this  effect  is 
the  same  as  would  be  produced  by  two  condensers, 
each  having  a  capacity  equal  to  half  that  of  the 
line,  shunted  across  the  line  at  the  receiving  and 
sending  ends  respectively.  The  effect  of  the  con- 
denser at  the  receiving  end  is  to  increase  both  the 


140 


ELECTRIC  POWER  CONDUCTORS 


equivalent  resistance  of  the  load  and  also  the  load 
power  factor;  the  condenser  at  the  sending  end 
has  no  effect  on  the  power  loss  and  line  drop,  but 
merely  increases  the  resultant  power  factor  at  the 
generating  end. 

TABLE  IV 

SIZE    AND    WEIGHT    OF    STRANDED    COPPER    AND    ALUMI- 
NUM WIRES 


Size  B.  &  S. 

Circ.  Mils. 

Diameter,  Ins. 

Lbs.  per  Mile.* 

Copper. 

Aluminum. 

1,000,000 

1.152 

16,140 

4,870 

9OO,000 

1.092 

14,53° 

4,380 

800,000 

'  I-°3S 

12,910 

3,890 

700,000 

0.963 

11,300 

3,410 

600,000 

0.891 

9,690 

2,920 

500,000 

0.819 

8,070 

2,43° 

450,000 

0.770 

7,260 

2,190 

400,000 

0.728 

6,460 

i,947 

350,000 

0.679 

5^50 

!,7°3 

300,000 

0.630 

4,840 

1,460 

250,000 

0.590 

4,040 

1,217 

oooo 

211,600 

°-53° 

3,420 

1,030 

000     , 

167,800 

0.470 

2,710 

817 

oo 

133,100 

0.420 

2,150 

648 

o 

105,500 

0-375 

i»7°3 

5i3 

i 

83,690 

0-330 

I»35I 

407 

2 

66,370 

o.  291 

1,071 

323 

4 

41,740 

0.231 

674 

203 

6 

26,250 

0.183 

420 

128 

*  Increased  i  %  over  weight  of  solid  wire  on  account  of  stranding. 


DETERMINATION  OF  SIZE  OF  CONDUCTORS  141 

In  addition  to  the  above  symbols  let 

b  ••=  capacity  susceptance  *  per  mile  of  two  parallel 
wires  for  a  frequency  of  one  cycle  per  second 
(Table  V) ; 

B  =nbL  for  a  three-phase  line  or  -    -  for  a  single-phase 

4 

line,  where  n  is  the  number  of  cycles  per  second, 
and  L  as  defined  above  is  the  length  in  miles  of 
each  wire  for  a  three-phase  line  or  the  length  of 
both  wires  for  a  single-phase  line. 

Then  the  equivalent  power  factor  at  the  receiving 
end  is  the  cosine  k'  corresponding  to  the  tangent  t' 

where 

BE2 


t'=t- 


W 


The  above  formulae  for  power  loss  and  pressure 
drop  (Case  I)  are  then  immediately  applicable,  sub- 
stituting for  k  and  t  the  values  kf  and  t' ;  the  formula 
for  predetermining  the  size  of  wire  in  terms  of  the 
pressure  drop  (Case  III)  may  also  be  applied,  assum- 
ing the  capacity  susceptance  equal  to  that  of  a 
No.  oooo  wire,  an  assumption  which  will  introduce 
but  a  slight  error,  since  the  capacity  susceptance 
varies  but  slightly  with  the  size  of  wire.  The  power 

factor   formula   ko  =     —-  k',  given   under   Case  I,   is 

*  b='LTzC  where  C  is  the  capacity  per  mile  in  farads  of  the  condenser 
found  by  each  pair  of  wires. 


142 


ELECTRIC  POWER  CONDUCTORS 


the  power  factor  at  the  generating  end  excluding  the 
second  condenser,  the  actual  power  factor  at  the 
generator  is  the  cosine  k'Q  corresponding  to  t'0  where 


t  o  =  fo  ~~ 


o' 


where  Wo  =  (i+Q)W,  the  total  power  supplied  at  the 
generating  end. 

TABLE  V 

CAPACITY  SUSCEPTANCE  PER  MILE  OF  TWO  PARALLEL 
STRANDED  WIRES  FOR  FREQUENCY  OF  ONE  CYCLE 
PER  SECOND 


Size  C.M. 


Distance  Apart  of  Wires  in  Feet. 


ana  ±J.  &  ^>. 

i. 

2. 

3- 

6. 

10. 

1,000,000 
500,000 
250,000 

9-3XIQ-8 
8.3Xio-8 
7.6Xio~8 

7-5Xio-8 
6.9Xio-8 
6.4Xio~8 

6.8Xio-8 
6.3Xio-8 
5-SXio-8 

5.8Xio~8 
5.4Xio8- 
S.iXio-8 

5-3Xio-8 
4.gXio~8 
4.yXio~8 

0000 

I 
6 

7-4Xio-8 
6.6Xio~8 
5-8Xio-8 

6.2Xio-8 
5-7Xio-8 
5.oXio-8 

5-7Xio-8 
5.2Xio-8 
4-yXio-8 

5.oXio~8 
4-6XIQ-8 
4.2Xio-8 

4.6Xio~8 
4-3Xio-8 
3-9Xio-8 

NOTE. — The  charging  current  per  mile  of  sine.le-ph.ase  line  (2  miles  of  wire^  is 
equal  to  io3XbnE;  for  a  three-phase  line  the  charging  current  per  wire  per  mile  of 
line  (3  miles  of  wire)  is  equal  to  1.16  X  io3nbE,  where  n  is  the  cycles  per  second,  b 
the  capacity  susceptance  given  in  the  table,  and  E  the  kilovolts  between  wires. 


A.  C.  Trolley.  The  resistance  and  reactance  of 
various  combinations  of  overhead  trolleys  and  zoo-lb. 
return  rails  are  given  in  the  Table  VI.  This  table  is 
based  on  extended  tests  made  by  A.  W.  Copley  on  the 
New  York,  New  Haven  and  Hartford  Railroad  and 


DETERMINATION  OF  SIZE  OF  CONDUCTORS   143 

other  single-phase  roads,  the  results  of  which  were 
published  in  the  Proceedings  of  the  American  Insti- 
tute of  Electrical  Engineers  for  December,  1908. 
Unfortunately  there  is  no  reliable  data  on  rails  of 
smaller  section,  but  as  the  greater  part  of  the  resist- 
ance is  in  the  trolley,  and  only  a  small  percentage 
of  the  total  reactance  is  due  to  the  magnetic  field  in 
the  rail,  the  values  given  for  the  combined  resistance 
and  reactance  respectively  may  also  be  used  with 
but  slight  error  in  case  the  rail  is  of  smaller  size.  It 
should  be  noted  that  the  reactance  for  the  three  sizes 
of  wire  given  are  constant  to  within  5%  for  any 
height  from  15  to  30  feet  above  the  track. 

The  figures  showing  the  division  of  current  between 
the  track  and  the  earth  refer  to  intermediate  por- 
tions of  long  sections  (over  three  miles) ;  a  greater 
portion  of  the  current  flows  in  the  track  near  the  load 
and  the  power  house.  It  will  be  noted  that  if  we  let 
pf  be  the  percentage  current  in  each  trolley  and  p" 
the  percentage  current  in  each  rail,  and  the  respective 
resistances  r'  and  rn ',  the  total  resistance  of  any  com- 
bination of  trolleys  and  rails,  as  measured  by  Mr. 
Copley,  is  approximately  prr'+p"r"\  similarly  the 
total  reactance  is  p'x'  +  p"x",  where  xf  and  x"  are  the 
reactances  of  a  single  trolley  and  rail  respectively ; 
using  these  formulae,  a  closely  approximate  value  for 
the  equivalent  resistance  and  reactance  for  any  other 
combination  of  trolleys  and  rails  for  any  division  of 
current  between  the  rails  and  the  earth  can  be  ob- 


144 


ELECTRIC  POWER  CONDUCTORS 


TABLE  VI 

RESISTANCE  AND  REACTANCE  OF  SINGLE-PHASE  TROLLEY 
WITH  loo-LB.  RAIL-RETURN 


Percent- 

Resistance Ohms  per  Mile. 

No.  of 
Tracks. 

No.  of 
Trolley 
Wires. 

No.  of 
Return 
Rails. 

age  of 
Current 
Return- 
ing this 

oooo  Trolley 

ooo  Trolley 

Rail. 

25  Cycles. 

15  Cycles. 

25  Cycles. 

12  Cycles. 

i 

.. 

0.26* 

0.26 

0-33 

°-33 

I 

100 

0.16* 

0.13 

0.16 

0.13 

I 

i 

25 

0.30 

0.29 

o-37 

0.36 

I 

Track  i 

2 

40* 

0.29* 

0.28* 

0.36 

o-35 

2 

"         2 

4 

58*. 

0-155* 

0.15* 

0.20 

0.19 

4 

"      4 

8 

75* 

0.086* 

0.082* 

O.II 

O.IO 

Resistance  Ohms 

Reactance  Ohms 

Percent- 

per Mile. 

per  Mile. 

No.  of 
Tracks. 

No.  of 
Trolley 
Wires. 

No.  of 
Return 
Rails. 

age  of 
Current 
Return- 
ing this 
Rail. 

oo  Trolley. 

No.  oooo,  No.  ooo  or 
No.  oo  Trolley. 

25  Cycles. 

12  Cycles. 

25  Cycles. 

12  Cycles. 

I 

.. 

... 

0.42 

0.42 

0.38 

0.23 

I 

100 

0.16 

0.13 

0.44 

0.26 

I 

I 

25 

0.46 

0-45 

0.49 

0.30 

I 

Track  i 

2 

40* 

0-45 

0.44 

0.47* 

0.282* 

2 

"         2 

4 

58* 

0.24 

0.23 

0.269* 

0.161* 

4 

"      4 

8 

75*    ' 

0.13 

0.12 

0.168* 

O.  IOI* 

NOTE. — The  figures  marked  thus  (*)  are  taken  directly  from  Mr.  Copley's  paper; 
the  others  are  derived  from  these.  At  the  point  where  the  current  enters  the 
rail  Mr.  Copley  found  that  70%  of  the  current  starts  toward  the  power  house  on 
a  singe  track  road  and  similarly  87%  on  a  four  track  road,  in  each  case  the  rail 
currents  falling  to  the  values  given  in  the  table  in  a  distance  of  about  three  miles 
and  from  that  point  on  remaining  practically  constant  until  near  the  power  house. 


DETERMINATION  OF  SIZE  OF  CONDUCTORS   145 

tained.  In  case  of  a  catenary  suspension  a  certain 
percentage  of  the  overhead  current  is  carried  by  the 
messenger  cable,  but  on  account  of  the  high  effective 
resistance  of  a  steel  cable  to  alternating  currents,  this 
current  will  be  quite  small.  (In  a  TV  messenger 
cable  carrying  a  No.  oooo  wire  Mr.  Copley  gives  the 
messenger  current  as  but  3.5%  of  the  total.) 

To  determine  the  power  loss,  pressure  drop,  etc., 
for  a  single-phase  trolley  system,  the  formulae  given 
above  under  Case  I  are  directly  applicable,  putting  L 
equal  to  the  distance  in  miles  of  the  load  from  the 
power  house  (or  substation)  and  r  and  x  equal  re- 
spectively to  the  combined  resistance  and  reactance 
of  trolley  and  track  per  mile,  as  given  in  Table  VI. 
Similarly,  the  proper  size  of  trolley  for  any  given  set 
of  conditions  can  be  determined  by  the  formulae 
given  under  Case  III,  taking  from  Table  VI  the  react- 
ance per  mile  (which  is  constant  for  the  three  sizes 
of  trolley  given  and  likely  to  be  used  in  good  practice), 
and  selecting  the  size  of  trolleys  from  Table  VI  corre- 
sponding to  the  value  of  the  resistance  per  mile  rit 
given  by  the  formula 


146  ELECTRIC  POWER  CONDUCTORS 


NUMERICAL  EXAMPLES 

Case  I.  A  load  of  5000  kilowatts  at  80%  factor 
is  to  be  delivered  at  40,000  volts  over  a  three-phase 
line  of  No.  2  B.  and  S.  copper  wire  30  miles  long, 
frequency  25  cycles  per  second,  wires  spaced  4  feet 
apart.  To  find  the  power  loss,  pressure  drop,  and 
power  factor  at  generating  end  we  have 

£=40; 


£=3°; 

r=o.8 

#=0.283  +  0.029  =0.312 


o 


Then 

08^2 

Power  loss       Q  =        •  =0.125, 
0.03 


•  * 
DETERMINATION  OF  SIZE  OF  CONDUCTORS   147 


Pressure  drop  P  =o.8v  (i.  125)2  +  (°-796)2  —  I  =0.102. 
Generator  power  factor 


£<,=—— +  0.8=0.817. 

1. 102 


Case  II.  A  load  of  5000  kilowatts  at  80%  power 
factor  is  to  be  delivered  at  40,000  volts  over  a  three- 
phase  line  of  copper  wire  30  miles  long,  allowable 
power  loss  12.5%.  To  find  the  size  wire  to  use,  we 
have 

£  =  40; 


£=3°; 

2  =  0.125; 

^(0^x40)* 

30X5 
Then,  using  the  formula  r  =  RQ, 

Resistance  per  mile  r  =  0.125  X  6.  83  =0.854, 

whence  from  Table  II  we  find  that  the  proper  size 
is  No.  2  B.  and  S. 

Case  III.  A  load  of  5000  kilowatts  at  80%  power 
factor  is  to  be  delivered  at  40,000  volts  over  a  three- 
phase  line  of  copper  wire,  30  miles  long,  frequency 


148  ELECTRIC  POWER  CONDUCTORS 

25  cycles  per  second,  wires  spaced  4  feet  apart,  allow- 
able pressure  drop  10.2%.  To  find  the  size  wire  to  use 
we  have 

£  =  40; 


P  =  o.io2  ; 
xi  -0.283; 

(0.8X4Q)',,, 

30X5 

71=0.75+^^-0.791 
0.53 


Then 
Resistance  per  mile 


-  i    =  0.880, 


whence  from  Table  II  we  find  the  nearest  size  wire 
is  No.  2  B.  and  S.  The  value  of  x2  corresponding  to 
TI  =0.880  is  0.030,  which  makes  ^  =  0.796  and  gives 
0.854  as  the  corresponding  value  for  r,  showing  that 
the  error  in  the  first  approximation  for  r  is  only  3%. 
The  above  example  may  also  be  used  to  illustrate 


*  * 
DETERMINATION  OF  SIZE  OF  CONDUCTORS   149 

an  extreme  case,  in  which  the  first  approximation 
for  r  may  be  entirely  erroneous,  but  by  successive 
applications  of  the  above  formula  a  correct  solution 
can  be  obtained. 

Keeping  the  other  conditions  the  same,  suppose  we 
change  the  frequency  to  125  cycles  per  second.     Then 

#1  =  1.413, 


First  approximation 


ri  -  6.83   >-  (°-957)2-  i        -0.060, 

which  shows  that  it  is  impossible  to  deliver  power 
under  the  conditions  stated  over  a  line  having  a 
reactance  as  great  as  that  of  a  No.  oooo  wire. 

As  a  second  approximation  assume  a  reactance 
equal  to  that  of  a  500,000  c.m.  wire.  The  resistance 
per  mile  then  works  out  0.041  ohm,  which  is  again 
too  small  a  value,  because  the  reactance  correspond- 
ing to  a  wire  having  this  resistance  is  less  than  that 
of  a  500,000  c.m.  wire. 

As  a  third  approximation  assume  a  reactance  equal 
to  that  of  a  700,000  c.m.  wire.  The  resistance  per 
mile  then  works  out  0.079,  the  reactance  of  which  is 
about  i%  less  than  that  of  the  700,000  c.m.  assumed. 


150  ELECTRIC  POWER  CONDUCTORS 

The  nearest  commercial  size  of  wire  corresponding  to 
a  drop  of  10.2%  is  700,000  circ.  mil. 

As  a  matter  of  fact,  however,  the  drop  for  any  size 
between  a  No.  oooo  wire  and  a  1,000,000  c.m.  wire 
would  be  substantially  the  same,  as  will  be  readily 
seen  by  calculating  the  drop  for  these  two  sizes  by 
the  exact  formula  of  Case  I,  which  gives  a  drop  of 
9.6%  for  a  1,000,000  c.m.  wire  and  13.0%  for  a 
No.  oooo  wire,  as  against  the  10.2%  specified.  There- 
fore, by  increasing  the  drop  to  13.0%,  say,  a  saving 
of  70%  in  copper  can  be  effected.  (Were  the  drops 
proportional  to  the  resistance  the  saving  in  the  copper 
for  the  same  increase  in  drop  would  be  only  21.5%.) 
Again,  the  use  of  two  circuits  of  No.  2  wire  each 
would  give  a  drop  of  but  9.5%,  and  would  effect  a 
saving  of  81.0%  in  copper. 

Case  IV.  Take  the  example  given  under  Case  I, 
but  assume  the  pressure  at  the  generator  44,080  volts, 
the  receiver  pressure  E  being  unknown.  Then 


2  x  3°  X  5 


(0.8)2(0.852  +0.312  ) 

-5^5- 
whence 


R  =3-45[I  +  ^i  -0.044]  =6.83, 

which  agrees  with  the  value  found  in  Case  I.     The 
power  loss,  pressure  drop   (as  a  fraction  of  the  de- 


DETERMINATION  OF  SIZE  OF  CONDUCTORS  151 

livered  pressure),  and  power  factor  at  generating  end 
then  work  out  the  same  as  in  Case  I.  The  pressure 
drop  as  a  fraction  of  the  pressure  at  the  generating 
end  is 

P  0.102 

—  —  =  ----  =  0.0926. 
1+P       1.  102 

Effect  of  Capacity.     Take  the  example  given  under 
Case  I.     From  Table  5 


whence    B  =  25  X  30  X  5.0  X  io~8  =  3  .8  X  io"5, 

3.8Xio-5X(4o)2 
and          £'=0.75--  -  =  0.738. 

£'=0.805;     (Table  III.) 
R_  (0.805  X4Q)2 
30X5 


Then 

Power  loss       Q—~-r — -  =  0.123, 
6.91 


Pressure  drop  P  =  0.805^(1.  123)2  +  (0.783)2—  i  =0.102 

£o  =  —-~X  0.805  =0.821; 
1.090 

*o=  0.683   (Table  III); 


5.02 

Generator  power  factor  £'0  =  0.831     (Table  III.) 


152  ELECTRIC  POWER  CONDUCTORS 

A.  C.  Trolley.  2000  kilowatts  are  to  be  supplied 
to  a  locomotive  at  90%  power  factor,  and  10,000 
volts  at  a  distance  of  twenty  miles  from  the  power 
house  (or  substation)  ;  No.  oooo  trolley,  return  cir- 
cuit two  100  Ib.  running  rails,  frequency  25  cycles. 
To  find  the  power  loss,  pressure  drop  and  power 
factor  at  power  house,  we  have,  assuming  the  divi- 
sion of  current  between  rails  and  earth,  as  given  in 
Table  VI, 


=  20 

k  =  o.g 
£  =  0.489 
r  =  0.29 

#  =  0.47 


20X2 


T  =  0.489+— =  0.718 


Then 


Power  loss       Q=——    =  0.141, 
2.05 


Pressure  drop  P  =  o. 9  V'(i.i4I)2  +  (°-7l8)2~  I  =0.213. 
Power  factor  at  power  house 

1.141 
1.213 


DETERMINATION  OF  SIZE  OF  CONDUCTORS  153 

Taking  the  reverse  problem,  suppose  that  we  wish 
to  determine  the  size  of  trolley  to  use  for  a  drop  of 
21.3%  between  power  house  and  locomotive,  the 
other  conditions  being  the  same  as  given  in  the 
preceding  example.  We  then  have  by  formula  under 
Case  III, 


^2—  )2-  (0.718)2-1]  =0.29, 


whence,  from  Table  IV,  the  proper  size  of  trolley  is 
a  No.  oooo. 

Transmission  Line  with  Resistance,  Reactance,  Leak- 
age, and  Capacity.  The  following  is  a  complete  solu- 
tion involving  no  approximations,  The  only  assump- 
tions made  are  that  the  resistance,  reactance,  leak- 
age, and  capacity  are  true  constants  and  that 
sufficient  time  has  elapsed  for  steady  conditions  to 
have  become  established. 

Let  E  =  volts   between   each   wire    and   neutral    at 

generator  end; 

I  =  amperes  per  wire  at  generator  end  ; 
cos  $  =  power  factor  at  generator  end  ; 

W  =  El  cos  (/>  =  total  watts  deliver  edto  line  per 

wire. 

These   same  symbols   with   the  subscript   "o"   refer 
to  the  receiver. 


r     TT-S  — 
Q     E02  cos 

receiver; 


=  equivalent  admittance  of  the 


154  ELECTRIC  POWER  CONDUCTORS 

r  =  resistance  of  each  wire  per  unit  length ; 
x  =  reactance  of  each  wire  per  unit  length ; 
z  =  vV2  +  x2  =  impedance   of   each   wire  per   unit 
length ; 

T  t  X\ 

cos  e  =-  =  power  factor  of  the  line  (sin  £  =-] ; 

z  \  z  / 

g  =  leakage  conductance  between  each  wire  and 

neutral  per  unit  length; 
b=  leakage  susceptance  *  between  each  wire  and 

neutral  per  unit  length ; 
y  =  \/g%  +  b2  =  leakage  admittance  per  unit  length ; 

cos  7)  =—  =  power  factor  of  leakage  circuit  I  sin  >?=—); 

L  =  length  of  line  in  any  unit. 
Calculate  the  following  quantities :  J* 


J 

-          and     r= 


2  2 

log  m  =  o.4343ayL  cos  /?; 
sin  ? 


U0=aY0', 

*b=27ifC  where/  is  the  frequency  in  cycles  per  second  and  C  the 
capacity  between  each  wire  and  the  neutral  per  unit  length. 

t  Greek  letters  are  used  to  represent  angles  in  degrees.  The  logarithm  is 
to  the  base  ten. 


DETERMINATION  OF  SIZE  OF  CONDUCTORS  155 

m    , =— — 


cos 


tfo, 

q=  —  Vi  +  t/o2  —  zU0  cos  ati. 
2m 

i-W 


49 
has  the  same  sign  as  <70. 


D  =     p2  +  q2  +  2pq  cosd; 


p2-q2 

rne>   f)  _  £_ 

DQ  • 

6  has  the  same  sign  as  d.     Then 
Volts  at  generator  end,  E  =  DEo 

Amperes  at  generator  end,  /  =  — 

Power  factor  at  generator  end,  cos  $  =  cos  (6  —  f) 

Total  watts  delivered  to  line,  W  =  EI  cos  0 

(End  of  H.  Fender's  article.) 

Voltage     Drop     and     Synchronous     Apparatus.       An 

excessive  ohmic  drop  in  the  transmission  lines  is 
liable  to  cause  hunting  of  rotary  converters  or 
synchronous  motors.  The  exact  amount  permissible 
depends  upon  the  design  of  the  rotary  converter, 
those  designed  for  normal  A.C.  starting  requiring 
less  drop  than  those  designed  for  D.C.  starting.  In 


156  ELECTRIC  POWER  CONDUCTORS 

the  latter  type  of  machine  an  ohmic  drop  of  20%  is 
generally  permissible  whether  or  not  a  simultaneous 
reactive  drop  exists.  Converters  of  the  A.C.  start- 
ing type,  do  not,  as  a  rule,  operate  satisfactorily  if 
the  ohmic  drop  is  so  high. 

6.     ECONOMICAL    SIZE    OF    CONDUCTORS.     (Kelvin's 

Law) 

The  total  expenditure  on  a  transmission  system 
is  made  up  of  the  initial  cost  plus  the  annual  expenses. 
The  most  economical  system  to  install  for  permanent  use 
is  that  in  which  the  sum  of  these  items  is  a  minimum. 

The  annual  expenses  consist  of  maintenance,  depre- 
ciation, and  power  lost  due  to  resistance. 

It  is  usual  to  reduce  the  initial  cost  to  a  yearly 
basis  for  purposes  of  comparison,  this  yearly  basis 
being  the  interest  which  must  be  paid  for  the  use 
of  the  money,  or  which  is  lost  by  withdrawing  the 
money  from  a  profitable  investment  and  putting  it, 
in  feeder  metal. 

As  a  rule,  it  is  necessary  to  work  out  the  sum  of 
the  expenses  for  various  sizes  of  wires  and  select 
that  size  which  gives  the  minimum  total  cost. 

When,  however,  the  capital  outlay  is  propor- 
tional to  the  amount  of  copper  in  the  system,  the 
following  law,  given  by  Lord  Kelvin,  is  of  use. 

'  The  most  economical  area  of  conductor  will  be 
that  for  which  the  annual  interest  on  capital  out- 
lay equals  the  annual  cost  of  energy  wasted." 


•   * 
DETERMINATION  OF  SIZE  OF  CONDUCTORS  157 

One  side  of  this  equation  would  be  the  interest, 
depreciation,  maintenance,  and  repairs;  the  other,  the 
cost  of  producing  energy  at  the  station  bus,  includ- 
ing interest,  depreciation,  and  operating  expenses. 

Kapp  has  made  Kelvin's  law  of  more  universal 
application  by  changing  it  to  the  following  form: 

"  The  most  economical  area  of  conductor  is  that 
for  which  the  annual  cost  of  energy  wasted  is  equal 
to  the  annual  interest  on  that  portion  of  the  capital 
outlay  which  can  be  considered  proportional  to 
the  weight  of  metal  used." 

The  simplest  way  of  applying  Kelvin's  law  is  that 
due  to  Dr.  Fender.  The  most  economical  current 
density  per  million  circular  mils  is 


A^c 

where  L  =  increase  in  annual  charges  on  transmis- 
sion line  resulting  from  increasing  the  weight  of 
feeders  one  ton  (2000  Ibs.),  and  C  =  increase  in 
annual  operating  and  capital  charges  on  the  power 
station  resulting  from  increasing  the  output  one 
kilowatt.  A  is  a  constant  whose  value  is 


i 
2170^ 


Weight  of  conductors,  Ibs.  per  cu.in. 
Specific  resistance,  ohms  per  mil-foot' 


For  copper,  A  =380 
Aluminum,    A  =  165 


158  ELECTRIC   POWER  CONDUCTORS 

Calculations  of  this  kind  are  often  rendered  use- 
less by  the  following  circumstances: 

1.  The   rate   of   interest   on   the   capital   outlay   is 
difficult  to  estimate  exactly. 

The  discount  of  bonds  depending  on  the  value 
below  par  at  which  they  are  sold  cannot  be  pre- 
dicted for  the  future. 

2.  The  life  of  insulation  is  difficult  to  estimate. 

3.  The  cost  of    copper,  lead,   and    insulation    con- 
stantly  fluctuates.     It   makes    a   material    difference 
in  the  depreciation  whether  the  price  of  copper  and 
lead  is  assumed  to  rise  or  fall  during  the  period  it  is 
in  use. 

4.  There  is  not  always  a  market  for  power  that 
can  be  saved  by  additional  feeder  metal. 

Owing  to  the  inaccuracy  of  these  premises,  it  is 
advisable  to  make  two  calculations,  using  for  one 
the  maximum  possible  value  of  L  and  the  minimum 
possible  value  of  (7,  and  in  the  other  the  minimum 
value  of  L  and  the  maximum  value  of  C. 

The  economical  current  density  will  then  be 
between  the  extremes  thus  obtained. 

It  is  thus  obvious  that  the  size  of  conductors  to 
be  used  is  more  a  matter  of  judgment  than  of  mathe- 
matics. 


CHAPTER  V 

DETERMINATION  OF  SIZE  FOR  GIVEN  STRESS 
IN  SPAN 

ALGEBRAIC  METHOD 

(Abstracted  by  permission  from  article  in  Electrical  World,  N.  Y.  Jan.  12, 
1907,  by  H.  Fender,  Ph.D.) 

Formulae  are  closely  approximate:* 

a  =  coefficient  of  expansion  of  wire  per  degree 
Fahrenheit ; 

D  =  deflection  of  wire  at  center  of  span  in  feet,  in 
the  direction  of  the  resultant   force    at    tem- 
perature t; 
*  =  length  of  span  in  feet ; 

M  -  modulus  of  elasticity  (pounds,  square  inches) ; 

m  =  weight  of  wire  per  cubic  inch  in  Ibs. ; 

p  =  ratio  of  the  resultant  of  weight  of  wire  and  sleet 
and  wind  pressure  to  the  weight  of  wire,  at 
temperature  /; 

Po  =  corresponding  ratio  at  temperature  t0 ; 

T  =  tension  at  center  of  span  in  thousands  of  Ibs. 
per  sq.in.  at  temperature  /; 

*  See  Appendix  V. 

159 


160  ELECTRIC  POWER  CONDUCTORS 

TQ  =  tension  at  center  of  span  in  thousands  of  Ibs. 
per  sq.in.  at  temperature  to] 

K     Pl- 
K~* 


o 

t  and  t0  described  above  under  D,  K,  K0,  T,  and 
TO,  and  are  in  degrees  Fahrenheit. 

General  Formulae  for  Points  of  Support  on  the  same  Level 


D  =  o.ooi$mlK. 
Copper  wire  :  * 


D  = 
Aluminum  wire:  f 

-K2o)  +  1965(70-  T)]. 


Making  numerical  calculations,  choose  various  val- 
ues for  T  and  plot  the  corresponding  values  of  /  in 
the  form  of  a  curve,  from  which  the  value  of  the 
tension  for  the  temperature  in  question  can  be  taken. 

*  For  Copper  for  which  1*1  =  0.321,  a  =  g.6Xio~6,  M=i2Xio°. 
f  For  Aluminum  for  which  ^=0.0967,  a=i2.8Xio-8,  M  =9X10'. 


SIZE  OF  GIVEN  STRESS  IN  SPAN  161 

The  value  of  K  is  obtained  from  this  value  of  T  and 
used  in  the  formula  for  D. 

GRAPHICAL  METHOD 

Instead  of  the  trial  method  above  outlined,  a 
graphical  method  giving  a  direct  answer  was  out- 
lined by  Dr.  Fender  in  the  Electrical  World,  Sept.  28, 
1907. 

The  two  charts,  Figs.  24  and  25,  are  the  essential 
parts  of  this  method.  (See  p.  172  for  method  of 
constructing  these  charts.) 

Calculation  of  Tension  and  Sag 

Given:  A  span  of  length  /  and  the  points  of  sup- 
port on  the  same  level ;  tension  7\ ;  ratio  of  resultant 
force  to  weight  of  wire,  pi.  To  find  the  tension  T 
when  the  temperature  rises  /  degrees  and  the  ratio 
of  resultant  force  to  weight  of  wire  changes  to  p  (for 
example,  sleet  melts  off). 

1.  On  the  line  corresponding  to  /  find  the  point  3 
having  the  abscissa  /  on  the  temperature  scale. 

2.  On  the  curve  corresponding  to  p\  find  the  point 
having  the  abscissa  T\  and  at  this  point  lay  off  the 
length  of  the  ordinate  of  point  3,  upward  if  /  is  posi- 
tive or  downward  if  t  is  negative. 

3.  Through  the  point  2  thus  obtained  draw  a  line 
parallel  to  the  line  /. 

4.  The  abscissa  of  the  point  4  where  this  line  cuts 


162 


ELECTRIC  POWER  CONDUCTORS 


SIZE  OF  GIVEN  STRESS  IN  SPAN 


163 


164 


ELECTRIC  POWER  CONDUCTORS 


the  curve  corresponding  to  p  is  the  tension  T  at  the 
new  temperature  when  the  ratio  of  the  resultant  force 
to  weight  of  wire  is  p. 

5.  The  abscissa  of  the  point  5  where  the  horizontal 
line  through  4  cuts  the  parabolic  curve  corresponding 
to  /  gives  the  corresponding  deflection  D  at  the  center 
of  the  span  in  feet. 

Instead  of  actually  drawing  the  straight  line  2-4  a 
pair  of  compasses  may  be  used;  i.e.,  lay  off  the  dis- 
tance 1-2,  then  open  the  compasses  until  the  lower 


FIG.  26. 

point  touches  the  straight  line  /;  then  keeping  the 
compasses  vertical,  slide  the  lower  point  along  I  until 
the  upper  point  intersects  the  curve  corresponding 
to  p.  If  t  is  negative,  i.e.,  if  the  temperature  de- 
creases, lay  off  1-2  in  the  opposite  direction. 

The  deflection   under  any  conditions   can  also   be 
calculated  from  the  formula 


when  T  is  known. 


•    * 
SIZE  OF  GIVEN  STRESS  IN  SPAN  165 

Calculation  of  p 

Let  a)  =  weight  of  wire  in  pounds  per  foot. 
The  weight  of  sleet  (and  hemp  core,  if  any)  in  pounds 
per  foot  of  wire  is 

a)i  =0.312  (d2i  -  d2)  +  0.3  2d2o, 

where  d  is  the  diameter  of  the  wire,  and  d\  the  diame- 
ter over  sleet  and  do  the  diameter  of  the  core,  all  in 
inches. 

The  wind  pressure  in  pounds  per  foot  of  wire  is* 


a>2  =  0.00021 
I 

where  V  is  the  actual  wind  velocity  in  miles  per  hour; 
di=d  in  case  of  no  sleet.  The  relation  between  indi- 
cated wind  velocity  (as  given  by  U.  S.  Weather 
Reports)  and  actual  velocity  is  as  follows: 

Indicated  Velocity.        Actual  Velocity.  0.0002  iF2. 

10  9.6  0.0194 

20  17.8  0.0667 

30  25.7  0.139 

40  33-3  °-233 

50  40.8  0.350 

60  48.0  0.485 

70  55.2  0.640 

80  62.2  0.812 

90  69.2  i.oi 

IOO  76.2  1.22 

*  H.  W.  Buck,  in  Transactions  International  Electric  Congress,  1904. 


166  ELECTRIC  POWER  CONDUCTORS 

The  ratio  p,  when  the  wind  is  horizontal,  is  then 


/       wA*     /o>2 
=  \/   I+"~)  +  (-~ 

\\  O)/  \W 


When  the  wind  is  acting  vertically  downward, 

0)1-}- 0)2 

p  =  i  + . 

0) 

Calculation  of  Sag  with  Wind  Blowing.  In  case 
of  no  wind,  or  the  wind  blowing  vertically  downward, 
the  vertical  sag  5  will  be  the  same  as  the  deflection 
D.  A  horizontal  wind  t  gives  a  horizontal  component 
to  the  resultant  force,  so  that  the  vertical  sag  when 
the  wind  is  blowing  horizontally  is 

D 


Example:  A  No.  oo  stranded  copper  cable  is  to 
be  strung  in  still  air  at  70°  F.  between  two  points 
on  the  same  level  800  ft.  apart,  so  that  at  a  tem- 
perature of  o°  F.,  with  a  coating  of  sleet  J  in. 
thick  all  around,  and  wind  blowing  horizontally 
directly  across  the  span  at  65  miles  an  hour  (actual 
velocity),  the  tension  in  the  cable  will  be  30,000  Ibs. 
per  sq.in. ;  (i)  at  what  tension  must  the  cable  be 
strung,  and  (2)  what  will  be  the  vertical  sag  at  string- 


•  * 
SIZE  OF  GIVEN  STRESS  IN  SPAN  167 

ing  temperature,  i.e.,  70°,  also  (3)  what  will  be  the 
sag  at  zero  temperature  when  the  cable  is  coated 
with  J  in.  of  sleet  and  wind  is  blowing  with  a  velocity 
of  65  miles  an  hour,  and  (4)  what  will  be  the  sag  as 
a  temperature  of  150°  in  the  still  air? 
We  have 

to  =0.406 


wi  =0.312(1. 418  -0.418  )  =0.574 

2 

W2  =0.00021  X&5  Xi.4iQ  =1.26. 


Therefore,  at  o°  with  wind  and  sleet 


(i)  Measure  off  with  compasses  on  Chart  No.  i  the 
vertical  distance  from  t  =  jo  on  X  axis  to  the  straight 
line  corresponding  to  /  =  800.  Lay  this  distance  off 
vertically  above  the  point  on  the  curve  correspond- 
ing to  ,0=3.93  having  the  abscissa  7^=30.  Keep 
the  upper  point  fixed,  open  the  compasses  until  the 
lower  point  touches  the  line  Z  =  8oo;  then,  keeping 
the  compasses  vertical,  slide  the  lower  point  along 
the  line  /=8oo,  until  the  upper  point  intersects  the 
curve  £  =  i  at  7^=8.35;  the  cable  must  therefore 
be  strung  at  a  tension  of  8350  Ibs.  per  sq.in.  This 
value  of  T  is  readily  checked  by  finding,  by  the  alge- 


168  ELECTRIC  POWER  CONDUCTORS 

braic    method    given    in    the    preceding    section,    the 
temperature  rise  corresponding  to  7^  =  8.35.     Thus, 

3-93X800 

AO  = =  104.0, 

30 

800 


I35(3°-8-35)  =2922; 
t-to  =o.o644(-  1837  +  2923)  =  70°, 

which  is  the  temperature  rise  given.  (2)  The  ab- 
scissa of  the  point  on  the  parabolic  curve  /  =  8oo, 
having  the  same  ordinate  as  the  point  corresponding 
to  <o  =  i  and  7  =  8.35  is  .0  =  36. 9  ft.,  which  is  the 
vertical  sag  5  in  still  air  at  70°  F. 

(3)  The  deflection  at  o°  with  sleet  and  wind  is 
the  abscissa  of  the  point  on  the  parabolic  curve 
/  =  800  having  the  same  ordinate  as  the  point  cor- 
responding to  po  -3.93  and  TO  =30,  i.e.,  A)=4°-4  ft. 

The  vertical  sag  is 

«•  40.4  __a4.8ft... 


(4)  To  find  the  sag  at  150°  proceed  as  under  (i) 
and  (2)  taking  t  =  i$o.  The  sag  will  be  found  to  be 
5=39.2  ft. 


SIZE  OF  GIVEN  STRESS  IN  SPAN  169 

Wire  Suspended  from  Points  Not  on  the  Same 
Level.  The  charts  also  apply  directly  to  the  deter- 
mination of  the  change  in  tension  in  spans  when 
the  points  of  support  are  at  different  heights.  In 
this  case,  however,  the  vertical  sag  Si  (=  deflection 
in  case  of  no  wind)  below  the  higher  point  of  sup- 
port, is  given  by  the  formula 


s,-s(,+As) 


where  h  is  the  difference  in  height  of  the  two  points 
of  support  and  5  is  the  vertical  sag  for  a  span  of 
equal  length  but  points  of  support  on  the  same  level; 
5  is  calculated  by  the  formula  given  above,  i.e., 


y 


1  + 


D  being  the  deflection,  taken  directly  from  the  chart, 
for  a  span  of  equal  length  but  points  of  support  on 
the  same  level;  in  case  of  no  wind  5  =D. 

The  distance  of  the  point  of  maximum    sag   from 
the  lower  point  of  support  is 


When  h  is  greater  than  45  the  lower  point  of  sup- 
port is  the  point  of  maximum  sag,  i.e.,  the  lowest 
point  in  the  span. 


170  ELECTRIC  POWER  CONDUCTORS 

Consider  three  consecutive  poles  A,  B,  and  C.  Let 
Z,  h,  and  5  refer  to  the  span  of  A  B,  and  /',  h'  ',  and  5' 
refer  to  the  span  BC,  where  5  and  5'  are  the  sags  for 
spans  of  length  /  and  I'  but  with  points  of  support 
on  the  same  level  and  h,  is  the  height  of  the  point  of 
support  at  A  above  the  point  of  support  at  B,  and  h' 
is  the  height  of  the  point  of  support  at  B  above  the 
point  of  support  at  C  ;  if  B  is  below  C,  h'  is  to  be  taken 
as  negative.  Then  the  total  vertically  downward 
pull  on  the  insulator  B  due  to  the  span  on  the  two 
sides  is 


where  W  is  the  weight  of  wire,  sleet,  and  vertically 
downward  wind  per  lineal  foot. 

If  the  quantity  in  the  bracket  is  negative  there 
will  be  an  upward  lift  on  the  insulator.  It  is  neces- 
sary to  apply  this  criterion  only  for  those  spans  for 
which  h  is  greater  than  4^;  if  h  is  less  than  45  for 
the  span  on  each  side  of  the  pole  B,  both  the  terms 


—  1    and    (i — )  in  the  above  expression 

457  \       45V 


are 


positive.  It  should  be  noted  that  the  sag  5  will  be 
a  minimum  when  the  temperature  is  at  its  lowest 
value,  but  no  sleet  on  the  wire,  and  the  wind  is  blow- 
directly  across  the  span  at  maximum  velocity;  the 
above  criterion  should  therefore  be  applied  for  these 
conditions.  (See  p.  176  for  graphical  method.) 


SIZE  OF  GIVEN  STRESS  IN  SPAN  171 

Example.  In  the  example  given  above,  suppose 
the  difference  in  height  of  the  points  of  support  is 
20  ft.  Then  (i)  the  tension  at  70°  will  still  be  8350 
Ibs.  per  sq.in.  (2)  The  corresponding  vertical  sag  at 
70°  in  still  air  for  points  of  support  at  same  level  is 
36.9  ft.f  therefore,  for  the  span  under  consideration 
the  vertical  sag  from  the  highest  point  of  support  is 


(3)  The  vertical  sag  at  o°  with  sleet  and  wind  for 
points  of  support  on  the  same  level  is  24.8  ft.  ;  there- 
fore, for  a  20-ft.  difference  in  the  height  of  points  of 
support  the  vertical  sag  from  the  highest  point  of 
support  is 


(4)  The  vertical  sag  at  a  temperature  of  150°  for 
points  of  support  on  the  same  level  is  39.2  ft.  ;  there- 
fore, for  a  2o-ft.  difference  in  height  of  the  points  of 
support  the  vertical  sag  from  the  highest  point  of 
support  is 


The   diagrams,    Figs.    24   and    25,    are   reduced   to 
such  a  small  scale  that  they  are  of  little  use  for  actual 


172  ELECTRIC  POWER  CONDUCTORS 

calculations.  It  is  therefore  necessary,  in  practical 
work,  to  draw  a  series  of  curves  of  suitable  scale. 
These  curves  are  plotted  from  the  following  equations : 

io9 

Inclined  straight  lines :  y  =  ^,-    070  T. 

6Mm2l2 

Parabolic  curves  on  left-hand  side:  D  =  o.ooi$ml2Vy. 
(D  is  measured  to  the  left  from  the  origin.) 

(P  \2 
Hyperbolic  curves  on  the  right-hand  side :   y  =  ( —  j  . 

Temperature  scale  *  on  the  axis  of  T:  x  =  io~3  Mat, 

Symbols  used  in  formulae  above : 
M  =  modulus  of  elasticity  of  wire,  Ibs.  per  sq.in. ; 
m  =  weight  of  wire  per  cubic  inch,  Ibs. ; 
/  =  length  of  span,  feet; 
T  =  tension  at  center  of  span,  thousands  of  Ibs.  per 

sq.in.; 

D  =  deflection  at  center  of  span,  feet; 
a  =  coefficient  of  expansion  of  wire  per  degree  F.; 
t  =  temperature  rise,  degrees  F.; 

p=  ratio  of  the  resultant  of  the  weight  of  wire,  the 
weight  of  sleet,  and  the  wind  pressure  to  the 
weight  of  wire; 

;y  =  an  arbitrary  quantity,  the  physical  meaning  of 
which  does  not  appear  in  the  calculations,  as  all 
the  quantities  entering  the  problem  are  given  as 
abscissae;  y  being  merely  a  common  ordinate 
for  all  the  curves. 

*  x  is  the  distance  on  the  scale  of  T  corresponding  to  the  temperature  /. 


SIZE  OF  GIVEN  STRESS  IN  SPAN 


173 


TABLE   GIVING   THE   VALUE   OF    T    FOR   VARIOUS   VALUES 
OF  p  AND  y=r 


Values 

Values  of  p. 

I  .0. 

I  .  2. 

1.4. 

1.6. 

1.8. 

2  .0. 

2  .  2. 

2.4. 

O.2 

0.17 
0.13 

2.24 
2-43 

2-77 

2.68 
2.91 
3-33 

3-40 
3-88 

3-58 

3-88 
4-44 

4.02 
4-37 
4-99 

4-47 
4-85 

5-55 

4.92 

5-34 
6.10 

5-37 
5-82 
6.66 

O.IO 

0.07 
0.04 

3^78 
5-oo 

3-79 
4-54 
6.00 

4-43 
5-29 
7.00 

5-o6 
6.05 
8.00 

5-69 
6.80 
9.00 

6-32 
7-56 

10.00 

6.96 
8.32 
ii  .00 

7-59 
9.07 

12.  OO 

0.03 

0.02 
0.017 

5-77 
7-°7 
7.67 

6.92 

8.49 
9.20 

8.08 

9-9° 
10.74 

9.24 
11.31 
12.27 

10.39 
12.73 
13.81 

"•55 
14.14 

12.70 
iS-S6 
16.87 

13-86 
16.97 
18.41 

0.014 
O.OI2 
0.010 

8-45 

10.00 

10.14 
10.95 

12.00 

11.83 

12.78 
14.00 

13-52 
14.61 
16.00 

15.21 
16.43 
18.00 

16.90 
18.26 
20.00 

18.59 

20.1 
22.  O 

20.3 

21.9 

24.0 

O.008 
O.006 
O.OO5 

ii.  18 
12.91 
14-14 

13-42 

J5-49 

16.97 

15-65 
18.07 
19.80 

17.89 
20.7 

22.6 

20.1 
23-2 
25-5 

22.4 
25-8 
28.3 

24.6 
28.4 

26.8 
31.0 

33-9 

O.OO4 
0.0035 
0.0030 

15.81 
16.90 
18.26 

18.97 

20.3 

21.9 

22.1 

23-7 
25-6 

25-3 
27.0 

29.2 

28.5 
30.4 
32.9 

31-6 
33-8 
36.5 

34-8 
37-2 
40.2 

37-9 
40.6 

43-8 

0.0025 
0.0020 
0.0015 

20.00 

22.4 
25-8 

24.0 
26.8 
31.0 

28.0 
36-1 

32.0 

35.8 

41-3 

36.0 
40.2 
46.5 

40.0 

44-7 
51-6 

44-0 
49-2 
56.8 

48.0 

53-7 
61.9 

O.OOIO 
0.0005 

31-6 

44-7 

37-9 
53-7 

44-3  x 
62.6 

50.6 

71.6 

56.9 

80.5 

63-2 
89.4 

69.6 
98-4 

75-9 
107.3 

174 


ELECTRIC  POWER  CONDUCTORS 


TABLE   GIVING   THE   VALUE   OF    T   FOR   VARIOUS   VALUES 
OF  p  AND  y  =(-£-]—  (Continued) 


Values 
of 

»-(£)* 

Values  of  p. 

2.6. 

2.8. 

3-0- 

3-2. 

3-4- 

3.6. 

3-8. 

4.0. 

0.2 

5-8i 

6.26 

6.7I 

7.16 

7.60 

8.05 

8.50 

8.94 

O.I7 

6.31 

6.79 

7-28 

7.76 

8.25 

8-73 

9-22 

9.70 

O.I3 

7.21 

7-77 

8.32 

8.87 

9-43 

9.98 

10.54 

II  .09 

0.10 

8.22 

8.85 

9-49 

10.12 

IO-75 

11.38 

12.02 

12.65 

0.07 

9.83 

10.58 

n-34 

12.10 

12.85 

13.61 

14.36 

15.12 

0.04 

13.00 

14.00 

15.00 

16.00 

17.00 

18.00 

I9.0O 

20.0 

0.03 

15.01 

16.16 

J7-32 

18.47 

19.63 

20.8 

21.9 

23-1 

O.O2 

18.38 

19.80 

21.21 

22.63 

24.0 

25-5 

26.9 

28.3 

O.OI7 

19.94 

21-5 

23.0 

24-5 

26.1 

27.6 

29.1 

3°-7 

O.OI4 

22.0 

23-7 

25-4 

27.0 

28.7 

3°-4 

32.1 

33-8 

O.OI2 

23-7 

25-6 

27-4 

29.2 

31.0 

32-9 

34-7 

36.5 

O.OIO 

26.O 

28.0 

30.0 

32.0 

34-o 

36.0 

38.0 

40.0 

0.008 

29.1 

3i-3 

33-5 

35-8 

38.0 

40.  2 

42.5 

44-7 

O.006 

33-6 

36-1 

38-7 

4i-3 

43-9 

46.5 

49-  1 

51-6 

O.OO5 

36.8 

39-6 

42.4 

45-2 

48.1 

50-9 

53-7 

56.6 

O.OO4 

41.1 

44-3 

47-4 

50.6 

53-8 

56-9 

60.  i 

63.2 

0.0035 

43-9 

47-3 

50-7 

54-1 

57-5 

60.8 

64.2 

67.6 

O.OO30 

47-5 

Si-i 

54-8 

58.4 

62.1 

65-7 

69-4 

73-o 

O.OO25 

52.0 

56.0 

60.0 

64.0 

68.0 

72.0 

76.0 

80.0 

0.0020 

58-1 

62.6 

67.1 

71.6 

76.0 

80.5 

85.0 

89-4 

0.0015 

67.1 

72-4 

77-4 

82.6 

87.8 

92-9 

98.1 

103.2 

O.OOIO 

82.2 

88.5 

94-9 

IOI.2 

i°7-5 

113.8 

120.2 

126.5 

0.0005 

116.3 

125.0 

134-2 

143  -1 

152.0 

161.0 

170.0 

178.9 

SIZE  OF  GIVEN  STRESS  IN  SPAN          175 

Relation    between    Sag  and   Length.      [Approximate 
method  based  on  parabolic  equation,  and  applicable 
only  when  tension  (Ibs.)  at  center  is  very  great  com- 
pared with  weight  of  wire  (Ibs.  per  foot)]. 
Let  5=  length  of  wire,  support  to  support; 

/=  horizontal  distance  between  supports; 
D  =  deflection   (in  same  units)  . 

8D2 
Then,  5  =/  +  -.— 

3    * 

[The  exact  method  is  based  on  the  catenary  equa- 
tions and  involves  hyperbolic  functions.] 

Equations  of  Elastic  Catenary 

Let  D  =  deflection  of  wire  at  center  of  span  in  feet  ; 

/  =  distance  between  supports,  feet; 
m  =  weight  of  wire  per  cu.in.  ; 
p=  ratio  of  the  resultant  of  weight  of  wire  and 

sleet  and  wind  pressure  to  the  weight  of 

wire  ; 

T  =  tension  at  center  of  span  in  Ibs.  per  sq.in.; 
5  =  length  of  wire,  support  to  support; 


Then  the  exact  formula  for  D  and  s  are 


176 


ELECTRIC  POWER  CONDUCTORS 


Tables  of  hyperbolic  functions  are  published  in  the 
Smithsonian  Tables. 

Vertical  Stresses  on  Poles.  Every  span  from  pole 
to  pole  is  part  of  a  large  imaginary  span,  as  shown 


FIG.  27. 

in  Fig.  27.  If  there  is  an  intermediate  pole  of  such 
height  as  to  just  touch  the  imaginary  span,  the 
outside  poles  will  carry  the  entire  load,  leaving  the 


FIG.  2\ 


intermediate  pole  unloaded.  This  condition  is  shown 
in  Fig.  28.  If  the  intermediate  pole  is  of  such  height 
as  to  bring  the  wire  above  the  imaginary  span,  the 


FIG.  29. 

intermediate  pole  will  carry  part  of  the  load,  a  con- 
dition illustrated  in  Fig.  29.  If,  on  the  other  hand, 
the  intermediate  pole  brings  the  wire  below  the 


SIZE  OF  GIVEN  STRESS  IN  SPAN          177 

imaginary  span,  there  will  be  an  uplift  at  the  inter- 
mediate pole,  tending  to  detach  the  wire  from  its 
insulator,  a  condition  illustrated  in  Fig.  30.  In 
practice,  the  imaginary  span  is  plotted  on  tracing 
cloth  to  the  same  scales  as  the  pole  line  plans,  and 
laid  upon  the  latter  so  as  to  determine  whether  there 
are  any  places  where  there  is  an  uplift  on  the  poles. 
If  any  such  places  are  discovered,  the  pole  heights 
should  be  altered. 


FIG.  30. 

The  greatest  care  should  be  taken  to  hold  the 
curve  with  its  base  line  horizontal.  The  test  curve 
should  be  plotted  from  the  following  equation: 

d_Wx\ 

d=rise,  feet,  measured  upward  from  lowest  point; 

W  =  weight  of  wire,  pounds  per  foot; 

F  =  tension  in  wire,  pounds,  corresponding  to  lowest 
temperature  and  wind  blowing  directly  across 
the  span  with  maximum  velocity  (the  uplift- 
ing tendency  is  greatest  for  this  condition) ; 

x  ••=  distance  from  center  of  span,  feet. 

While  the  above  curve  is  only  approximate,  it  is 
so  close  to  the  exact  catenary  that  for  ordinary 


178 


ELECTRIC  POWER  CONDUCTORS 


working  tensions  it  cannot  be  distinguished  from 
the  latter. 

The  numerical  value  of  the  upward  pull  on  the  insula- 
tor may  be  calculated  as  follows,  referring  to  Fig.  3 1 : 

If  the  pole  C  were  removed,  the  span  LC  would 
support  the  span  CO,  0  being  the  lowest  point  of 
the  curve.  Since,  however,  the  span  CO  does  not 
exist,  pole  C  takes  the  force  exerted  by  the  span  LC, 
which  is  equal  to  the  weight  of  wire  from  C  to  0. 


FIG.  31. 

Pole  C  also  supports  the  length  CO',  found  by  sliding 
the  test  curve  along  until  it  touches  the  tops  of  C 
and  R\  the  weight  of  this  length  CO'  is  accordingly 
subtracted  from  the  weight  CO  in  order  to  obtain  the 
total  uplift  at  C. 

The  exact  equation  for  the  curve  of  sag  is 


p 
where    k  =T^T,    and    the    hyperbolic    cosines,    written 

"  cosh,"    may    be    obtained    from    the    Smithsonian 
Physical  Tables. 


CHAPTER  VI 
SPECIFICATIONS 

i.  CABLES  FOR  AERIAL  LINES 

IN   writing  specifications  for  bare  wire  cables  for 
aerial  lines  the  following  points  should  be  noted:* 

(1)  Service  to  be  used  for. 

(2)  Conductors. 

(a)  Solid  or  stranded. 

(6)   Number  of  wires  in  strand. 

(c)  Material  of  wires,  aluminum,  hard-drawn 

or  soft-annealed  copper. 
(It  is  usual  in  copper  cables  for  aerial  use 
to  have  the  central  wire  medium  soft, 
and  the  outers  hard;  sometimes  a  core 
of  hemp  is  used  in  place  of  the  central 
wire.) 

(d)  Combined  area   of   wires   when  laid  out 

straight  and  measured  at  right  angles 
to  their  axes. 

(e)  Pitch  of  each  layer  of  wires. 

(/)    Conductivity   in   terms   of    Matthiessen's 
Standard  for   soft-annealed   copper  as 

*  See  Appendix  VI. 

179 


180  ELECTRIC  POWER  CONDUCTORS 

given  in  the  A.I.E.E.  Standardization 
Report. 

(3)  Strength. 

(a)  Hard-drawn  copper  or  aluminum. 

The  tensile  strength  shall  be  not  less  than 

Ibs.  per  sq.in.       Elastic  limit 

shall  not  be  less  than  ...  Ibs 

Ibs.  per  sq.in.,  with  an  elongation  of  not 
less  than  .  .  .  %. 
(6)  Annealed  copper. 

Tensile  strength  shall  be  not  less  than 

.  .  .  Ibs.  per  sq.in.  with  an  elongation  of 

not  less  than  ...  %  in  a  five-foot  length. 

Elastic  limit  shall  be  not  less  than  .  .  .  Ibs. 

per  sq.in. 

It  is  usual  to  have  a  "  flexibility  "  test,  such  as  a 
requirement  that  each  of  the  wires  composing  the 
strand  shall  be  capable  of  being  wrapped  around  a 
wire  of  its  own  diameter  in  a  spiral  of  six  turns, 
without  surface  injury  or  cracking.  This  test  should 
be  performed  at  32°  F. 

The  finished  cable  shall  be  sufficiently  flexible 
between  the  temperatures  of  o°  F.  and  150°  F.,  so 
that  it  may  be  bent  around  a  cable  of  its  own 
diameter  without  injury  to  the  cable  so  bent. 

The  necessary  apparatus  for  making  all  tests 
shall  be  furnished  by  the  contractor. 

(4)  Length  of  cable  to  be  supplied  on  each  reel. 


••    * 

SPECIFICATIONS  181 

(5)  The  length  of  cable  on  each  reel  shall  be  con- 
tinuous;   there  shall  be  no  joints  or  splices  either  in 
the  cable  as  a   whole  or  in  the  individual  wires  of 
the  strand. 

(6)  Aluminum    cables   shall   be   without   dents   or 
scratches  which  might  impair  their  strength. 

(7)  The  cross-section  of  the  cable  shall  not  exceed 
the  specified  amount  by  over  2%. 

2.  INSULATED  CABLE 

TITLE 
Issue  No  ......  Date  ............ 

General.     This  cable  will  be  used 

(1)  In  tile  ducts; 

(2)  Buried  in  the  ground; 

(3)  Under  water; 

(4)  In  iron  or  fiber  pipes  ; 


(5)  In  iron  or  fiber  pipes  subjected  to 


to  carry 


vibration ; 

(6)  On  poles  and  supported  by  mes- 

senger wire ; 

(7)  In  the  open  air. 
f(i)  Direct; 

1  (2)    ...  .phase,  .  .  .  .cycle  alternating 
at  a  normal  working  voltage  of  ....  volts. 

All  workmanship  and  materials  shall  be  first- 
class  and  shall  be  in  entire  accord  with  the  best 
engineering  practice. 


\  current 


182 


ELECTRIC  POWER  CONDUCTORS 


Form    of    Cable.     (In  the  case  of  single  conductor 
cable).     The  cable  shall  consist  of 

f(i)  The  specified  number  of   ]  f  (i)  hard 


(2)  soft 


drawn 


.wires  each 


and 


[  (2)   (State  number) 
copper  wires 

(1)  Stranded  concentrically 

(2)  Rope  laid  in.  .  .strands  of 
insulated  with 

(1)  Paper 

(2)  Rubber 

(3)  Varnished  cloth 

(In  case  of  two  conductor  cables.) 

The  cable  shall  be  of  oval  form  and  shall  consist 
of  two  insulated  conductors  and  tarred  jute  laterals 
bound  together  with  cotton  tape  thoroughly  sat- 
urated with  rubber  compound. 

Each  conductor  shall  consist  of  wires 

stranded  into  cable. 

(In  case  of  multiple  conductor  cables.) 

The  cable  shall  consist  of  ....  (state  number) 
conductors  insulated  from  one  another  with 

(1)  Paper; 

(2)  Rubber;  and   stranded    into   cable 

(3)  Varnished  cloth, 
with  jute  laterals. 

Each  conductor  shall  consist  of  ....  (state  num- 
ber) wires  stranded  into  a  cable. 

(In  the  case  of  cables  having  several  layers,  as  for 
example,  in  control  cables,  add  following  clauses.) 


SPECIFICATIONS  183 

The  outer  layer  of  conductors  shall  have  a  covering 
of  tarred  rope.  Adjacent  layers  shall  be  wound  in 
opposite  direction,  and  around  each  layer  there  shall 
be  a  spiral  of  insulating  tape.  Each  layer  shall  in- 
clude one  conductor  differently  colored  from  the 
others. 

The  group  of  conductors  shall  have  a  belt  of 
(state  material)  insulation. 

Conductors.  The  conductors  shall  have  a  mini- 
mum conductivity  of  ninety-eight  (98)  per  cent,  Mat- 
thiessen's  standard,  as  given  in  the  A.  I.E.  E.  Stand- 
ardization Report,  for  soft  drawn  copper  wire,  and 
(if  rubber  or  cambric  insulated)  shall  be  provided 
with  a  heavy  uniform  coating  of  tin  without  pro- 
jections. 

The  combined  area  of  the  wires,  composing 
each  conductor,  when  laid  out  straight  and 
measured  at  right  angles  to  their  axes,  shall  be 

not  less  than  circular  mils  (No B. 

and  S.). 

Insulation.  The  insulation  (around  each  conduc- 
tor) shall  be  not  less  than  of  an  inch  thick, 

and  shall  consist  of 

(i)  Paper; 


(2)  Rubber; 


conforming  with  the  accom- 


(3)  Varnished  cloth, 
panying  insulation  specification. 

The  insulating  belt  shall  be  not  less  than    ....   of 
an  inch  thick,  and  shall  consist  of 


184  ELECTRIC  POWER  CONDUCTORS 

(i)  Paper; 


(2)  Rubber; 


conforming  with  the  accom- 


(3)  Varnished  cloth, 
panying  insulation  specification. 

Taping  and  Braiding.  The  cable  shall  be  taped 
and  braided  in  accordance  with  the  following  table 
(give  table  stating  number  of  layers  of  taping  and 
braiding) . 

The  tape  shall  be  of  closely  woven  cotton  filled 
with  rubber  compound,  and  shall  lap  at  least  one- 
third  its  width,  making  a  smooth  surface.  Layers 
in  double  taping  to  be  wound  in  opposite  directions. 

(If  cable  is  to  be  braided  use  the  following) : 

(Optional.)  Eight-ply  jute  thoroughly  tarred  shall 
be  applied  spirally  over  the  taping. 

(i)  Double  cotton 


A  braiding  of 


(2)  Six-lea  hemp 


saturated 


(3)    ...   inch  asbestos 
with    high    flash-point    coal    tar-compound    shall    be 

applied  over  the     /.    T   '         \.     The  compound  shall 
I  (2)  Jute       J 

neither  be  injuriously  affected  by  nor  shall  have 
injurious  effect  upon  the  materials  of  the  cable  at 
any  temperature  below  200°  F. 

Sheath.  A  sheath  consisting  of  an  alloy  of  tin  and 
lead  containing  not  less  than  ninety- eight  (98)  per 
cent  pure  lead  and  from  one  (i)  to  two  (2)  per  cent 
tin  shall  be  applied  uniformly  over  the  insulation. 
The  thickness  of  the  sheath  shall  be 


•  * 
SPECIFICATIONS  185 

(1)  ....  of  an  inch. 

(2)  According  to  the  following  table. 

(Give  table  of  sheath  thickness  for  different  sizes 
of  cable.) 

Armor.  (For  rubber  or  varnished  cloth  without  sheath.) 

The  above  cable  shall  be  protected  by  a  double 

taping  of  galvanized  steel   ....   inch  wide  and   

of  an  inch  thick  applied  in  such  a  manner  that  the 
spiral  space  between  adjacent  turns  shall  be  not 
more  than  one-eighth  (J)  of  an  inch;  the  outer  taping 
to  entirely  cover  the  spiral  space  left  between  the 
turns  of  the  inner  taping. 

(For  lead-sheathed  cables) : 

The  sheath  shall  be  protected  by  two  layers  of 
asphalted  or  tarred  jute  having  a  combined  thickness 
of  three-sixteenths  (3/i6)  of  an  inch,  and  shall  be 
armored  with  galvanized  mild  steel  wire  not  smaller 

than  No B.  and  S.     Over  the  armor  there  shall 

be  a  similar  covering  of  jute,  the  layers  of  which 
shall  be  wound  in  opposite  directions. 

Tests.  Factory  tests  to  be  made  in  the  presence 
of  the  company's  inspector. 

(Rubber  or  varnished  cloth  insulation) : 

The  electrical  tests  shall  be  made  upon  the  cable 
after  twenty-four  (24)  hours'  immersion  in.  water 
before  the  lead  sheath  or  braiding  is  applied. 

(Paper  insulation) : 

The  electrical  tests  shall  be  made  upon  the  cable 
after  it  has  been  (i)  passed  through  a  bath  of  water 


186  ELECTRIC  POWER  CONDUCTORS 

not  less  than  six  feet  in  length  and  of  sufficient 
depth  to  submerge  the  cable;  (2)  immersed  in  water 
for hours. 

(Paper  or  varnished  cloth) : 

A  high  potential  test  of  ....  volts  alternating  shall 
be  applied  for  a  period  of  ....  minutes  between 

(1)  Conductor  and  sheath; 

(2)  Conductors  and  between  conductors  and  sheath 
(the  latter  for  multiple  conductor  cables). 

(Where  cable  has  braid  or  steel  armor  instead  of 
sheath,  substitute  braid  or  armor  for  sheath.) 

The  insulation  resistance  after  one  minute's  elec- 
trification with  a  battery  of  not  less  than  one  hundred 
(100)  or  more  than  five  hundred  (500)  volts  shall  be 
measured  and  reduced  to  sixty  (60)  degrees  F. 
and  shall  not  be  less  than 

(1)  Is  required  for  successful  operation. 
(To  be  used  for  varnished  cloth.) 

(2)  Specified  in  insulation  specification  No 

(3)    megohms  per  mile. 

Each  finished  cable  shall  be  sufficiently  flexible 
between  the  temperatures  of  zero  and  one  hundred 
degrees  F.  so  that  it  may  be  bent  to  a  radius  of 

f  (i)  .  .times  its  diameter  1 

\  ,  \  without  miury. 

[  (2)    inches  J 

(The  apparatus  required  for  making  all  tests  shall 
be  furnished  by  the  contractor.) 

(Field  tests  to  be  made  in  the  presence  of  the  con- 
tractor's inspector.) 


SPECIFICATIONS  187 

Capacity  Guarantee.  The  contractor  shall  state  in  his 
proposal  the  guaranteed  electrostatic  capacity  of  the 
cables  at  60°,  100°,  and  150°  F.  under  the  following 
tests:  (i)  Each  conductor  against  the  . other (s)  and 
lead  sheath;  (2)  Between  (any)  two  conductors;  (3) 
Between  any  conductor  and  lead  sheath.  (If  braided 
or  taped  instead  of  sheathed,  use  corresponding  word 
instead  of  "  lead  sheath  "  above.) 

Inspection.  Cables  furnished  under  this  specifica- 
tion shall  be  available  for  inspection  during  the  process 
of  manufacture  except 

The  contractor  shall  notify  the  company  when  the 
manufacture  of  cable  is  to  begin  in  order  that  inspec- 
tion may  be  arranged  for. 

Data.  The  manufacturer  shall  supply  the  following 
data: 

(a)  Weight  per  foot. 

(b)  Diameter  of  wire. 

(c)  Diameter  of  cable  over  all. 

(d)  Diameter  of  splice. 

(e)  Length  of  splice. 
Installation  in  Ducts: 

(a)  By  whom  cable  is  to  be  installed. 

If  installed  by  cable  contractor  the  following  clauses 
are  necessary : 

(b)  By  whom  cable  lengths  will  be  determined. 

(c)  By  whom  ducts  will  be  rodded  and  wired. 

(d)  By  whom  terminal  end  bells,  clamps,  etc., 

will  be  supplied  and  erected. 


188  ELECTRIC  POWER  CONDUCTORS 

(e)    Type  of  joint. 

(1)  Sleeve  or  interlaced  strands. 

(2)  Compound  to  be  used. 

(3)  Material  of  taping,  paper,  cambric, 

or  rubber. 

(/)  By  whom  cables  will  be  racked  in  splicing 
chambers. 

(g)  Limit  to  number  of  splices  per  cable  per- 
missible in  one  splicing  chamber;  usu- 
ally one. 

(h)  How  and  by  whom  cable  sheaths  will  be 
grounded.  Description  of  ground  con- 
nections. 

(i)  How  and  by  whom  cables  will  be  wrapped 
or  otherwise  protected  in  splicing 
chambers. 

(/)  Contractor  shall  furnish  and  install  bush- 
ings or  cushions  for  the  cables  where 
they  leave  the  ducts. 

(k)  Contractor  shall  tag  every  cable  in  splicing 
chamber  and  station  with  a  brass  tag 
having  the  cable  number  stamped  on  it. 

(/)  Contractor  shall  refill  sleeves  after  .... 
months  if  any  perceptible  settlement 
has  taken  place. 

(m)  Tests.  A  high  potential  test  of  .... 
volts  alternating  shall  be  applied  for 

a  period  of  minutes  between 

conductors  and  sheath. 


•  * 
SPECIFICATIONS  189 

The  insulation  resistance  after  one  minute's  elec- 
trification with  a  battery  of  not  less  than  one  hun- 
dred (100)  or  more  than  five  hundred  (500)  volts, 
shall  be  measured  and  reduced  to  sixty  (60°)  F., 

and  (i)  shall  be  not  less  than    megohms  per 

mile,  (2)  shall  decrease  at  a  rate  not  exceeding 

per  cent  per  annum. 

3.   THIRTY  PER  CENT  PARA  RUBBER  INSULATION 

The  following  specification  is  offered  by  the  author 
as  more  suitable  for  obtaining  a  high  grade  insulation 
than  that  of  the  Rubber  Covered  Wire  Engineers 
Association  given  below. 

Description  of  Insulation.  Insulation  supplied  under 
this  specification  shall  contain  not  less  than  thirty 
(30)  per  cent  and  not  more  than  thirty-three  (33)  per 
cent  by  weight  of  rubber.  All  the  rubber  shall  be  the 
finest  dry  Para  gum,  which  has  not  previously  been 
used  in  rubber  compound.*  The  gum  itself  shall  not 
contain  more  than  three  (3)  per  cent  of  acetone  extract. 
The  compound  shall  be  properly  vulcanized,  and  after 
vulcanization  shall  contain  not  more  than  two  (2)  per 
cent  by  weight  of  acetone  extract  which  is  volatile  below 
212°  F.,  and  not  more  than  one  (i)  per  cent  of  free 
sulphur.  The  insulation  must  be  tough,  elastic, 
and  homogeneous,  and  placed  concentrically  about 

*  This  may  be  objected  to  by  certain  manufacturers  who  claim  the  use 
of  shoddy  to  be  beneficial. 


190  ELECTRIC  POWER  CONDUCTORS 

the    cable.     (The    thickness    specified    in    the    tables 
below  means  the  minimum  thickness  at  any  point.*) 

If  exigencies  of  manufacture  require  repairs  or 
joints  in  the  insulation,  the  entire  material  of  such 
joints  shall  conform  with  the  specification,  except 
that  over  thirty-three  (33)  per  cent  of  rubber  may  be 
used  and  the  work  shall  be  done  in  such  a  way  as  to 
leave  the  repaired  part  or  joint  as  strong  and  durable 
electrically  and  mechanically  as  the  remainder  of 
the  insulation. 

Tests.  The  electrical  tests  shall  be  made  upon 
the  cable  after  twenty-four  hours'  immersion  in 
water  and  before  the  braid  or  sheath  is  applied.  The 
high  potential  test  voltages  shall  be  applied  for  a 
period  of  one  minute.  The  insulation  resistance 
shall  be  measured  following  a  one-minute  electri- 
fication with  a  battery  of  not  less  than  100  and  not 
more  than  500  volts,  and  the  results  corrected  to 
the  standard  temperature  of  60°  F.  In  the  case 
of  cables  made  up  of  separately  insulated  wires 
or  cables,  the  insulation  resistance  test  shall  be 
made  before  assembling  the  wires;  the  high  potential 
test  shall  be  made  both  before  assembling  and  after 
the  cable  is  complete.  The  insulation  resistance  shall 
be  not  less  than  that  given  in  the  accompanying 
tables.  (Tables  should  be  prepared  as  under  "  Rub- 
ber Insulation,"  p.  84.) 

The  change  in  insulation  resistance  with  tempera- 

*  Optional. 


•  * 
SPECIFICATIONS  191 

ture  shall  be  at  a  rate  in  accordance  with  the  table 
herewith,  which  is  based  on  a  rate  of  two  and  six- 
tenths  (2.6)  per  cent  per  degree  F.  between  the  limits 
of  forty  (40)  and  seventy -five  (75)  degrees  F. 

A  sample  of  the  insulation  of  the  thickness  of 
the  insulating  wall,  without  taping,  shall  be  taken 
from  the  cable  and  cut  to  such  a  width  as  to  give  a 
cross-sectional  area  of  about  one-thirty  second  0/32) 
sq.in.  If  the  total  cross  section  of  insulation  is  less 
than  this,  the  whole  of  the  insulation  shall  be  used. 
Marks  shall  be  placed  two  (2)  ins.  apart  on  the  sample, 
which  shall  then  be  stretched  until  the  marks  are 
six  (6)  ins.  apart,  and  one  end  immediately  released; 
five  seconds  after  release  the  marks  shall  be  not 
over  two  and  three-eighths  (2!)  ins.  apart,  except 
as  noted  below.  The  sample  shall  then  be  stretched 
until  the  marks  are  eight  (8)  ins.  apart,  and  one 
end  immediately  released;  five  seconds  after  release, 
the  marks  shall  be  not  over  two  and  five-eighths 
(2 1)  ins.  apart,  except  as  noted  below.  Should  the 
cable  be  insulated  with  over  twelve  sixty-fourths 
(12/64)  ins.  of  rubber,  the  stretching  may  be  meas- 
ured thirty  seconds  after  release.*  Any  sample  may 
be  stretched  until  the  marks  are  nine  (9)  ins.  apart, 
before  breaking.  The  tensile  strength  of  the  com- 
pound shall  be  not  less  than  eight  hundred  (800) 
Ibs.  per  sq.in. 

*  The  stretch  test  may  be  made  less  severe  if  the  insulation  is  intended  for 
high  voltages. 


192 


ELECTRIC    POWER  CONDUCTORS 


These  conditions  shall  be  satisfied  at  any  temperature 
between  fifty  (50)  and  one  hundred  (100)  degrees  P., 
and  none  of  the  samples  shall  have  been  stretched  at 
all  prior  to  the  commencement  of  these  tests. 

The  necessary  apparatus  for  making  all  tests 
shall  be  furnished  by  the  contractor. 

Inspection.  The  contractor  shall  afford  every 
facility  for  the  engineer  to  assure  himself  that  the 
specified  'proportion  and  quality  of  rubber  is  put 
into  the  compound. 

TEMPERATURE  COEFFICIENT  OF  RESISTANCE 
30%  PARA  RUBBER  COMPOUND 


Tempera- 
turet 
Degrees  F. 

Coefficient 
shall  be  not 
greater  than 

Tempera- 
ture, 
Degrees  F. 

Coefficient 
shall  be  not 
less  than 

40 

.68 

60 

I.  000 

41 

.64 

6l 

0.974 

42 

.60 

62 

0.949 

43 

-56 

63 

0.925 

44 

-52 

64 

0.901 

45 

.48 

65 

0.878 

46 

-44 

66 

0-855 

47 

.41 

67 

0-833 

48 

-37 

68 

0.812 

49 

-34 

69 

0.791 

5° 

-3° 

70 

0.771 

Si 

-27 

7i 

0-751 

S2 

.24 

72 

0.732 

53 

.20 

73 

0-713 

54 

-17 

74 

0-695 

55 

.14 

75 

0.677 

56 

.11 

57 

.09 

58 

.06 

59 

-°3 

60 

.00 

SPECIFICATIONS  193 

The  insulation  resistance  (megohms)  at  a  given 
temperature  may  be  reduced  to  that  at  60°  Fahr. 
by  dividing  by  the  coefficient  corresponding  to  that 
temperature. 

4.  RUBBER  COVERED  WIRE  ENGINEERS'  ASSOCIATION 

SPECIFICATIONS   FOR   THIRTY   PER    CENT  RUBBER 
INSULATING  COMPOUND 

The  compound  shall  contain  not  less  than  30% 
by  weight  of  fine  dry  Para  rubber  which  has  not 
previously  been  used  in  rubber  compounds.  The 
composition  of  the  remaining  70%  shall  be  left  to 
the  discretion  of  the  manufacturer. 

Chemical.  The  vulcanized  rubber  compound  shall 
contain  not  more  than  6%  by  weight  of  acetone 
extract.  For  this  determination  the  acetone  extrac- 
tion shall  be  carried  on  for  five  hours  in  a  Soxhlet 
extractor,  as  improved  by  Dr.  C.  O.  Weber. 

Mechanical.  The  rubber  insulation  shall  be  homo- 
geneous in  character,  shall  be  placed  concentrically 
about  the  conductor,  and  shall  have  a  tensile  strength 
of  not  less  than  800  pounds  per  square  inch. 

From  any  wire  on  which  the  wall  of  insulation  does 
not  exceed  4/32  inch,  a  sample  of  vulcanized  rubber 
compound  not  less  than  4  inches  in  length  shall  be 
cut  with  a  sharp  knife  held  tangent  to  the  copper. 
Marks  should  be  placed  on  the  sample  2  inches  apart. 
The  sample  shall  be  stretched  until  the  marks  are 
6  inches  apart  and  then  immediately  released;  one 


194  ELECTRIC   POWER  CONDUCTORS 

minute  after  such  release  the  marks  shall  not  be  over 
2 1  inches  apart.  The  sample  shall  then  be  stretched 
until  the  marks  are  9  inches  apart  before  breaking. 

In  case  the  wall  of  insulation  exceeds  4/32  inch, 
the  return  required  shall  be  2\  inches  instead  of 
2  f  inches  and  the  stretch  before  breaking  shall  be 
8  inches  instead  of  9  inches. 

For  the  purpose  of  these  tests,  care  must  be  used 
in  cutting  to  obtain  a  proper  sample,  and  the  manu- 
facturer shall  not  be  responsible  for  results  obtained 
from  samples  imperfectly  cut. 

These  tests  shall  be  made  at  a  temperature  not  less 
than  50°  F. 

For  high  tension  service,  it  is  recommended  that 
the  above  mechanical  requirements  of  the  rubber  be 
eliminated. 

Electrical.  Each  and  every  length  of  conductor  shall 
comply  with  the  requirements  given  in  the  following 
table.  The  tests  shall  be  made  at  the  works  of  the 
manufacturer  when  the  conductor  is  covered  with  vul- 
canized rubber  and  before  the  application  of  other 
covering  than  tape  or  braid. 

Tests  shall  be  made  after  at  least  twelve  hours'  sub- 
mersion in  water  and  while  still  immersed.  The 
voltage  specified  shall  be  applied  for  five  minutes. 
The  insulation  test  shall  follow  the  voltage  test,  shall 
be  made  with  a  battery  of  not  less  than  100  nor 
more  than  500  volts,  and  the  reading  shall  be  taken 
after  one  minute's  electrification.  Where  tests  for 


SPECIFICATIONS  195 

acceptance  are  made  by  the  purchaser  on  his  own 
premises,  such  tests  shall  be  made  within  ten  days  of 
receipt  of  wire  or  cable  by  purchaser. 

Inspection.  The  purchaser  may  send  to  the  works 
of  the  manufacturer  a  representative  who  shall  be 
afforded  all  necessary  facilities  to  make  the  above 
specified  electrical  and  mechanical  tests,  and  also  to 
assure  himself  that  the  30%  of  the  rubber  above 
specified  is  actually  put  into  the  compound,  but  he 
shall  not  be  privileged  to  inquire  what  ingredients  are 
used  to  make  up  the  remaining  70%  of  the  compound. 

For  insulation  thickness  and  test  voltages  recom- 
mended by  the  Rubber  Covered  Wire  Engineers 
Association,  see  p.  86. 

5.  VARNISHED  CAMBRIC   INSULATION 

The  insulation  shall  consist  of  closely-woven  cotton 
tape  filled  and  uniformly  coated  with  a  solid  film 
of  insulating  compound.  The  tape  shall  be  applied 
spirally  with  turns  overlapping  and  successive  layers 
staggered.  Groups  of  layers  may  be  wound  in  oppo- 
site directions.  Between  the  layers  of  tape  there 
shall  be  a  film  of  waterproof,  viscous,  slow-drying  and 
adhesive  compound.  Should  the  contact  of  copper 
with  this  insulation  give  rise  to  any  injurious  re- 
action, a  separator  shall  be  applied  between  insula- 
tion and  copper.  The  insulation  shall  not  deteriorate 
at  a  constant  temperature  of  150°  F. 


196  ELECTRIC   POWER  CONDUCTORS 

6.    PAPER  INSULATION 

Shall  consist  of  the  best  grade  of  Manila  paper, 
containing  no  particles  of  iron,  wood  pulp,  or  any 
trace  of  alkali  or  acid,  and  shall  not  be  injured  by 
a  continued  temperature  of  130°  F.  The  paper 
shall  be  applied  spirally  with  turns  overlapping  and 
successive  layers  staggered  and  shall  be  saturated 
with  an  insulating  compound. 

Splicing  sleeves  shall  be  filled  with com- 
pound. (For  example,  paraffin  wax,  Voltax,  G.  E. 
No.  67,  ozite,  etc.  The  object  of  specifying  this  is  to 
secure  uniformity.)  * 

7.  RAIL  BONDS 

(1)  Style  of  Adhesion: 

(a)   Expanded  terminal. 
(6)   Compressed  terminal. 

(c)  Soldered. 

(d)  Brazed. 

(e)  Amalgam,  or  plastic. 

(2)  Location  to  be  Applied: 

(a)  Exposed. 

(b)  Concealed. 

(c)  Head. 

(d)  Web. 

(e)  Foot. 

*  This  clause  omitted  unless  cable  contractor  is  to  install  the  cable. 


SPECIFICATIONS  197 

(3)  Type  of  Conductor: 

(a)  Ribbon. 

(b)  Cable. 

(c)  vSolid. 

(4)  Size: 

(a)  Cross-sectional    area    measured    at    right 

angles  to  axes  of  individual  strands. 

(b)  Formed  length  between  centers  of  termi- 

nals, or  end  to  end. 

(c)  Contact  area  of  stud  or  other  contact  sur- 

face. 

(5)  Material.    The  bond  shall  be  of  copper  having 
a  conductivity   of    98%,    Mathiessen's    standard,   for 
soft-drawn  copper  wire,  A.  I.  E.   E.   Standardization 
Report. 

8.  HIGH  TENSION  LINE  INSULATOR 

1 i )  Service  to  be  used  for. 

(a)  Voltage. 

(b)  A.  C.  or  D.  C. 

(c)  Size  of  cable  to  be  carried. 

(2)  Number  of  pieces. 

(3)  General    dimensions    according    to    accompany-' 
ing    drawings.     Permissible    variation    from    dimen- 
sions on  drawings. 

(4)  Color  (usually)  white  or  chocolate  brown. 

(5)  Quality    of    material.     The    insulator    shall    be 
of  porcelain   (or  other  specified  material)   free  from 


198  ELECTRIC   POWER  CONDUCTORS 

pits,  cracks,  and  other  imperfections,  and  the  mate- 
rial shall  be  sound  throughout.  The  rest  marks  (on 
which  the  insulator  is  supported  in  glazing)  shall 
be  not  larger  than  ....  by  ....  inch. 

(6)  Tests.  The  contractor  shall  furnish  for  test 
....  per  cent  of  the  insulators  from  each  furnace 
charge  (if  porcelain). 

(a)  Absorption  Test. 

The  test  insulators  shall  be   broken  and 
the  exposed  surfaces  moistened  with  red 
ink.     If  the  ink  spreads  or  is  absorbed 
the  insulators  will  be  rejected. 
(6)  Structure. 

The  fracture  shall  exhibit  surfaces  free 
from  cracks,  blow  holes,  etc.,  and  hav- 
ing a  close  uniform  grain. 
The  following  tests  shall  be  made  on  all  insulators: 

(c)  The     insulator     (complete     and     assem- 

bled) shall  be  inverted,  immersed  in 
water  up  to  the  center  of  the  side  wire 
groove,  and  the  pin-hole  filled  with 
water  to  the  top  of  the  thread.  With 

kilo  volts    (A.   C.)    applied    for 

one  minute,  there  shall  be  no  indica- 
tion of  breakdown,  leakage,  or  exces- 
sive brush  discharge. 

(d)  Mounted   on   an   upright   metal   pin   and 

subjected  to  a  precipitation  of   

in.  (say  f  in.)  fresh  water  per  minute, 


SPECIFICATIONS  199 

the  insulators  shall  not  break  down  or 

arc  over  at  less  than   kilovolts 

between  pin  and  side  wire  groove. 
Tests  may  also  be  required  for  the  individual  shells 

of  which  the  insulator  is  built  up. 

If  the  insulator  is  of    the  Hewlett   type,   use   the 

following  clauses  instead  of  (c)  and  (d). 

(e)    The   insulator    (complete    and    assembled 
shall    be   subjected   to    a  potential    of 

kilovolts  A.  C.  applied  between 

opposite  wire  holes,  the  upper  one  being 
filled  with  water.  After  one  minute 
exposure  to  this  voltage,  there  shall  be 
no  indication  of  breakdown,  leakage, 
or  excessive  brush  discharge. 
(/)  The  insulator  (complete  and  assem- 
bled), subjected  to  a  precipitation  of 
....  in.  (say  J  in.)  fresh  water  per 
minute,  shall  not  break  down  or  arc 
when  exposed  to  a  potential  difference 

of    kilovolts   between   opposite 

holes. 


CHAPTER  VII 
TESTING  OF  WIRES  AND  CABLES 

WHEATSTONE'S  BRIDGE. 

Resistance. 

Inductances. 

RESISTANCE  BY  AMMETER  AND  VOLTMETER. 
RESISTANCE  BY  DIFFERENTIAL  GALVANOMETER. 
RESISTANCE  BY  SUBSTITUTION. 
STANDARD  RESISTANCES. 
PLUG  RESISTANCE  Box. 
REICHSANSTALT  RESISTANCES. 
SHUNTS. 

CAPACITY  BY  DIRECT  DISCHARGE. 
INSULATION  RESISTANCE  BY  DIRECT  DEFLECTION. 
VOLTMETER  TEST  OF  INSULATION  RESISTANCES. 
LOCATING  FAULTS. 

Murray  Loop  Test. 

Fisher  Loop  Test. 

Varley  Loop  Test. 

Point  by  Point  Method. 

WHEATSTONE'S  BRIDGE  OR  CHRISTIE'S  BRIDGE 

Resistance  Measurements.  Two  conducting  branches 
(Fig.  32)  PSQ,  PTQ,  are  joined  in  parallel,  and  a  current 
sent  through  the  arrangement,  as  indicated  by  the 
arrows,  then  in  passing  from  P  to  Q,  either  along  the 

200 


TESTING   OF   WIRES   AND  CABLES          201 

conductor  PSQ,  or  along  the  conductor  PTQ,  there  are 
points  having  all  potentials  between  the  potential  of  P 
and  that  of  Q,  therefore  it  follows  that  for  every  point 
in  the  conductor  PSQ  there  must  be  a  point  in 
the  conductor  PTQ  having  the  same  potential.  Let 
5  and  T  be  two  such  points;  then,  if  they  were 
joined  with  the  terminals  of  a  galvanometer,  there 
would  be  no  deflection.  Given  one  point  5,  the 
corresponding  point  T  can  therefore  be  experimentally 


FIG.  32. 

found  by  joining  one  terminal  of  a  galvanometer 
to  5,  and  touching  the  other  conductor  PTQ  at 
different  points  with  a  wire  attached  to  the  other 
terminal  of  the  galvanometer,  until  a  point  T  is 
found  for  which  there  is  no  deflection. 

Let  A  be  the  current  flowing  in  PSQ,  B  the  cur- 
rent flowing  in  PTQ,  and  a,  b,  c,  d  the  resistances 
respectively  of  PS,  SQ,  PT,  TQ\  then,  since  the 
potential  difference  between  P  and  5  is  the  same  as 
between  P  and  T, 


202  ELECTRIC   POWER  CONDUCTORS 

Similarly   since   the   potential    difference   between   5 
and  Q  is  the  same  as  between  T  and  Q, 

Ab  =  Bd. 
Hence, 

-  =  -     (Adapted  from  W.  E.  Ayrton's  "  Practical 
o     a 

Electricity.") 

Inductance  Measurements.  Place  the  inductance  to 
be  measured  in  one  arm  of  a  Wheatstone's  bridge 
and  balance  the  bridge  with  a  steady  current. 
Then  replace  the  simple  galvanometer  by  a  ballistic 
one  and  place  a  key  in  the  battery  circuit.  Upon 
depressing  the  key  •  the  galvanometer  needle  will 
swing  6  degrees.  Now  destroy  the  balance  of  the 
bridge  by  inserting  a  resistance  r  in  the  same  arm 
as  the  inductance,  and  note  the  permanent  deflec- 
tion <£.  Then 

1       -sin    0 


tan 
where 

T  =  time  of  natural  swing  of  galvanometer  needle. 

RESISTANCE  BY  AMMETER  AND  VOLTMETER 

This  method  is  generally  used  for  resistances  from 
.001  ohm  to  .01  ohm,  using  a  milli-  voltmeter  and  an 
ammeter.  By  Ohm's  law, 

Millivolts 


Ohms  = 


i  ooo  X  amperes' 


TESTING*  OF   WIRES   AND  CABLES 


203 


For  low-resistance  work  care  should  be  exercised 
that  the  voltmeter  reading  is  taken  across  the  resist- 
ance to  be  measured,  not  including  the  ammeter. 


RESISTANCE  MEASUREMENT  BY  DIFFERENTIAL 
GALVANOMETER 

The  arrangement  of  circuits,  as  shown  in  Fig.  33, 
is    the    simplest.     The    adjustable    resistance    R    is 


FIG  33. 

varied  until  the  galvanometer  show^s  no  deflection, 
when  R  is  equal  to  x. 

If  the  resistance  to  be  measured  is  small  in  com- 
parison with  that  of  the  galvanometer,  a  reversing 
switch  should  be  used,  enabling  readings  to  be  taken 
with  the  current  in  either  direction  through  the 
galvanometer  coils.  The  true  resistance  will  be  the 
mean  of  the  resistances  found  before  and  after  re- 
versal of  current.  The  connections  for  this  test 
are  shown  in  Fig.  34. 


204 


ELECTRIC   POWER  CONDUCTORS 


RESISTANCE  MEASUREMENT  BY  SUBSTITUTION 

A  battery  giving  a  constant  E.M.F.,  a  galva- 
nometer, an  adjustable  resistance,  and  the  resist- 
ance to  be  measured  are  all  connected  in  series. 
The  adjustable  resistance  is  short  circuited  and  the 
deflection  of  the  galvanometer  noted.  The  unknown 
resistance  is  then  short  circuited  and  the  adjustable 


FIG.  34. 

resistance  cut  in  until  the  same  deflection  is  obtained. 
The  resistance  thus  cut  in  equals  the  unknown 
resistance.  The  measured  resistance  should  be  large 
in  comparison  with  the  total  resistance  of  the  cir- 
cuit; this  method  is  therefore  suitable  for  measuring 
insulation  resistance  of  machines  and  cables.* 

*  See  p.  210. 


TESTING   OF   WIRES   AND  CABLES          205 

ACCURACY  OF  RESISTANCE  MEASUREMENTS 

(W.  E.  Ayrton,  Electrician,  London,  1907). 

By  comparison  with  a  standard  ohm,  a  resistance 
of  one  ohm  may  be  obtained  accurately  to  Vioo  of  i%, 
whereas  a  resistance  of  V  10,000  ohm  could  be  obtained 
accurately  to  only  about  i%. 

STANDARD  RESISTANCES 

The  standard  ohm  represented  by  a  column  of 
mercury  is  replaced  in  practice  by  coils  of  high 
resistance  wire  with  a  small  temperature  coefficient 
such  as  manganin,  platinoid,  or  German  silver. 

PLUG  TYPE  RESISTANCE  BOX  (Fig.  35) 

A  resistance  box  of  the  plug  type  contains  coils 
of  wire  Ci,  6*2,  etc.,  wound  on  insulating  bobbins. 
The  ends  of  these  coils  are  soldered  to  stiff  wires,  w, 
which  are  fastened  to  the  brass  pieces,  bi,  b2t  b3t 
which  are  screwed  to  the  insulating  top  of  the  box. 
When  a  plug  P  is  inserted  tightly  between  the  con- 
tact pieces  bi  and  62,  the  coil  c\  is  short-circuited 
and  practically  all  the  current  takes  the  short  path 
through  the  plug.  If,  however,  a  plug  is  withdrawn, 
as  at  A/",  all  the  current  passes  through  the  coil  C2. 
Hence  in  a  box  containing  coils  of  various  resistance, 


206 


ELECTRIC   POWER  CONDUCTORS 


by  taking  out  one  or  more  plugs,  the  resistance  in 
the  circuit  may  be  varied  at  will.  The  brass  contact 
pieces  are  shaped  to  form  a  space  5,  in  order  to 
render  the  surface  of  the  box  accessible  for  cleaning. 
The  number  near  each  plug  indicates  the  resist- 
ance which  is  put  in  circuit  when  the  plug  is  taken 
out. 

CD 


When  put  in  the  hole,  a  plug  should  be  given  a 
slight  downward  screwing  motion,  which,  if  the  plug 
is  properly  made,  should  make  it  hold  firmly. 

Coils  are  wound  double  so  as  to  form  a  loop  at  one 
end  and  two  free  ends  at  the  other.  This  makes  the 
current  flow  around  the  bobbin  an  equal  number  of 
times  in  each  direction  and  nullifies  the  magnetic 
effect,  thereby  rendering  the  coil  practically  non- 


TESTING?  OF   WIRES   AND   CABLES          207 

inductive    and    preventing    any    magnetic    action  on 
neighboring  instruments. 


REICHSANSTALT  RESISTANCES 

Standard  resistances  of  very  low  value,  say  less 
than  one- tenth  ohm,  cannot  be  satisfactorily  made  in 
the  ordinary  form,  owing  to  the  errors  introduced  by 
the  contact  devices  and  leads.  Instead,  the  resistance 
between  two  points  on  a  conductor  is  used,  and  the 
conductor  made  suitable  for  large  currents.  Current 
is  sent  through  a  pair  of  large  terminals  and  the 
drop  between  the  two  small  terminals  taken. 


SHUNTS 

Resistance  boxes  are  sometimes  made  up  as  ad- 
justable shunts  for  decreasing  the  current  in  a  galva- 
nometer in  a  kno\vn  ratio. 

Let  C\  =  current  in  unshunted  galvanometer; 
C2=  current  in  shunted  galvanometer; 
g  =  resistance  of  galvanometer; 
5  =  shunt  resistance ; 
m  =  resistance    of    remainder    of    circuit    (see 

Fig.  36). 
Then 


208 


ELECTRIC   POWER  CONDUCTORS 


With  the  arrangement  shown  in  Fig.  36,  calcula- 
tions have  to  be  made  for  every  combination  of 
galvanometer  and  resistance,  as  the  effect  of  the 
shunt  depends  on  both  the  galvanometer  and  out- 
side resistance.  The  Ayr  ton  &  Mather  Universal 
Shunt,  which  is  shown  diagramatically  in  Fig.  37, 
can  be  used  with  any  galvanometer,  and  circuit 


FIG.  36. 


FIG.  37. 


without  calculation.     In  order  to  obtain  1/i0,   Vino, 
or  Viooo  of  the  current  when  unshunted,  it  is  only 
necessary  to  pull  out  the  plug  corresponding  to  that 
fraction.     Referring  to  Fig.  37, 
R=  resistance  of  galvanometer 
r  =  resistance    of    shunt    coil,    which    is    connected 
permanently    across    the    galvanometer    dur- 
ing the  tests. 
/i  =  current  in  A  if  opposite  main  is  connected  to  the 

other  end  of  r\ 
72=  current  in  mains  A  and  B\ 


TEST  ING*  OF   WIRES   AND  CABLES          209 

B  is  any  variable  point  which  divides  r  into   two 

r        .  n  —  i 
parts  having  resistances  -  and  -     -  r,  respec- 

tively. 
d  =  galvanometer    current  with    mains    connected 

across  r\ 
C2  =  galvanometer  current  with  mains  connected  to 

A  and  B. 

Then, 


The  use  of  the  universal  shunt  produces  less  change 
in  the  resistance  of  the  circuit  from  its  original  value 
than  the  employment  of  the  ordinary  shunt,  pro- 
vided that  r  is  less  than 


g(n 


TESTING  CAPACITY  BY  DIRECT  DISCHARGE 

Apparatus.  Ballistic  galvanometer  and  standard 
condenser. 

Method.  Obtain  galvanometer  constant  by  noting 
deflection  d,  due  to  the  discharge  of  the  standard 
condenser  after  a  charge  of  say  ten  seconds  from  a 
given  E.M.F.  Then  discharge  the  unknown  capacity 


210 


ELECTRIC   POWER  CONDUCTORS 


through  the  galvanometer  after  ten  seconds'  charge 
and  note  the  deflection  d'  '.     Then, 


Capacity  =C—, 
C  being  the  capacity  of  the  standard  condenser. 


INSULATION  RESISTANCE  BY  DIRECT  DEFLECTION 

Referring  to  Fig.  38, 


G  is  a  mirror  galvanometer, 

S  is  a  shunt  for  the  above, 

B  is  a  battery  giving  between  100  and  500  volts, 

R  is  a  resistance  box  of   100,000  ohms, 

D  is  a  battery  reversing  key, 

C  is  a  short  circuit  key  for  galvanometer. 


TESTING  *OF   WIRES   AND   CABLES          211 

(i)   Put    the    switch    A    to    the    lower   point,    and 

using  -  of  the  number  of    cells   to  be   used  in  the 
n 

cable  test,  obtain  the  galvanometer  deflection. 

G  deflection  X  5  X  r  X  n 


Galvanometer  const.  = 


1,000,000 


where  r  is  the  resistance  unplugged  in  the  resistance 

box, 
5  is  the  multiplying  value  of  the  shunt. 

The  1,000,000  is  to  reduce  megohms. 

(2)  Put    the    switch    A    to    the    upper    point    and 
disconnect  the  lead  b  from  the  cable.     Upon  depres- 
sing the  key  D,  the  insulation  resistance  of  the  lead 
b    may    be    determined   from    the    deflection    of    the 
galvanometer.     The  deflection  should  be  zero,  but  if 
not,     it    should    be    deducted    from    the    deflection 
obtained  when  testing  the  cable. 

(3)  Close  switch  C  and  connect  b  to  cable. 

(4)  Open  C  carefully  to  see  if  there  are  any  earth 
currents.     If  any,  note  deflection  due  to  them,  and 
deduct  from   battery  reading  if  in  the  same  'direc- 
tion, or  add  to  it  if  in  opposite  direction. 

(5)  Close  C,   depress  one  knob  of  D,   using,   say, 
the    Vioo   shunt.     After   a   few   seconds    open   C;    if 
the  spot  goes  off  the  scale,  use  a  higher  shunt;    if 
the  deflection  is  low,  use  a  lower  shunt.     After  one 
minute's  electrification,  note  the  deflection. 


212  ELECTRIC   POWER  CONDUCTORS 

The    insulation    resistance    in   megohms, 

constant 
deflection  X  shunt' 

(6)  It  is  desirable  to  take  readings  at  the  end  of 
two,    three,    or    even    four    and    five    minutes.     The 
deflection  should  gradually  decrease. 

(7)  It  is  desirable  to  repeat  operations    with   the 
battery  reversed;     if    there    are    no    earth    currents 
the  readings  with  opposite  poles  of  battery   to  the 
cable   should   not   differ   appreciably. 

The  last  two  and  the  fourth  operations  are  unnec- 
essary for  tests  on  cables  in  tanks. 

This  method  is  the  one  universally  used  for  power 
cable  testing. 

VOLTMETER  TEST  FOR  INSULATION  RESISTANCE 

Connect  one  voltmeter  between  bus  and  cable 
sheath,  and  a  second  voltmeter  between  bus  and  con- 
ductor. 

Let  Vi=  volts  between  bus  and  cable  sheath. 
1/2=  volts  between  bus  and  conductor. 
r=  resistance    of    voltmeter    on    which  V2  is 

read,  ohms. 

R  =  megohms  between  conductor  and  sheath. 
L  =  Length  of  cable,  miles, 


"  Megohms  per  mile  "  =RxL. 


TESTING  OF   WIRES   AND  CABLES 


213 


LOCATING  FAULTS 

Murray  Loop  Test.  This  test  is  applicable  when 
a  good  wire  is  available,  having  practically  the  same 
resistance  as  the  faulty  wire,  a  condition  which 
occurs  when  the  fault  is  on  one 

ru-n 

wire  of  a  duplex,  triplex,  or 
other  multiple  conductor  cable. 
The  apparatus  being  connect- 
ed, as  shown  in  Fig.  39,  the 
resistance  R  is  varied  until  the 
galvanometer  is  not  deflected 
in  either  direction. 

L=  combined  length  of  good 
and  bad  wire  (equal  to 
twice  the  length  of  cable 
in  case  of  multiple  con- 
ductor cable) . 


o 


Distance  to  fault  = 


AL 
A+R' 


mimr 

FIG.  39. 


if  the  leading  wires  are  very  short.  If  the  leading 
wires  are  of  the  same  size  as  the  conductors  in  the 
cable, 

A 


Distance  to  fault  = 


A+R 


(L  +  S+T)-S. 


If  the  leading  wires  are  different  in  size  from  the 
cable  wires,  for  S   and   T  must  be  substituted  the 


214 


ELECTRIC   POWER  CONDUCTORS 


length  of  a  wire  of  the  same  size  as  that  of  the  cable 
wire  which  will  have  a  resistance  equal  to  that  of  5 
and  T  respectively. 

Fisher  Loop  Test.  This  test  is  applicable  when  there 
are  two  good  conductors  parallel  to  the  faulty  one. 
The  resistance  of  all  three  conductors  can  differ 
without  affecting  the  test. 


Ground  Connection 


JrlG.  41. 

The  apparatus  being  connected  as  shown  in  Fig.  40, 
with  the  switch  5  thrown  down,  the  resistance  R  is 
varied  until  the  galvanometer  shows  no  deflection. 
Then  switch  5  is  then  thrown  up  and  the  value  of 
RI  found  in  like  manner. 


Then  the  distance  to  the  fault 


Ai(A+R) 


— L,  where 


TESTING  *OF   WIRES   AND   CABLES          215 

L  =  length  of  the  faulty  conductor,  and  A  \  the  value 
of  A  when  the  variable  resistance  is  R\. 

This  method  is  applicable  to  the  locating  of  crosses 
if  the  lower  terminal  of  the  switch,  instead  of  being 
grounded,  is  connected  to  the  wire  crossed  with  the 
one  used  in  the  test. 

Varley  Loop  Test.  The  apparatus  being  connected 
as  shown  in  Fig.  41,  where  the  faulty  conductor  is 
shown  on  the  left-hand  side,  the  resistance  R  is  ad- 
justed so  that  the  galvanometer  is  not  deflected, 
and  a  record  made  of  the  respective  values  of  A, 
B,  and  R.  Then  measure  the  combined  resistance 
of  the  two  conductors  of  the  cable  and  of  a  and  fr,  the 
leads  from  the  testing  resistances  R  and  A  respectively, 
to  the  cable.  Let  this  be  r,  and  let  x  be  the  resist- 
ance of  the  conductor  as  far  as  the  fault.  Then 

Br-AR 

%  =  — - — — a. 

A  +  B 

The  resistances  a  and  b  are  obtained  by  the  use  of 
the  Wheatstone's  bridge,  the  dotted  line  battery 
connection  being  used  and  the  ground  connection 
taken  off  the  battery. 

The  above  method  is  also  applicable  for  locating 
a  cross  between  two  wires,  if  a  connection  to  the 
wire  which  is  crossed  be  substituted  for  the  ground 
connection. 


216  ELECTRIC   POWER  CONDUCTORS 


LOCATING  FAULTS  BY  POINT-BY-POINT  METHOD 

The  cable  fault-locating  outfit  of  the  New  York 
Interborough  Rapid  Transit  Company  consists  essen- 
tially of  a  Brush  D.  C.  arc  generator  fitted  with  a 
current  reversing  device,  this  being  located  in  the 
power-station,  and  of  a  current  detector  used  outside 
along  the  cable  line. 

One  terminal  of  the  generator  is  connected  to  the 
cable  to  be  tested  and  the  other  terminal  grounded 
to  the  sheath  of  the  cable.  The  slowly  alternating 
current  from  the  reversing  device  is  revealed  by  the 
current  detector  if  the  latter  is  placed  near  the  cable 
between  the  power-station  and  the  fault;  beyond  the 
fault  the  current  indicator  should  show  no  signs  of 
the  slowly  alternating  current. 

The  Brush  generator  is  a  9.6  ampere  machine 
giving  a  maximum  of  4000  volts.  It  is  direct  driven 
by  a  50  H. P.  three-phase  induction  motor. 

The  reversing  device,  from  the  mechanical  stand- 
point, consists  of  a  wooden  cylinder,  about  8  inches 
diameter  and  18  inches  long,  mounted  on  a  horizontal 
shaft  set  in  brass  bearings  and  fitted  with  a  gear 
wheel  operated  by  a  worm  on  the  shaft  of  a  small 
induction  motor.  The  entire  cylinder  and  appurte- 
nances are  immersed  in  oil  and  contained  in  a  closed 
cast  iron  box.  The  general  appearance  is  shown  by 
Fig.  42- 


TESTING  ,OF   WIRES  AND  CABLES          217 


The  electrical  features  consist  of  three  brass  rings 
each  |  inch  wide  by  \  inch  deep,  screwed  to  the  cylin- 


nduction  Motor 


SECTION  OF  CURRENT  REVERSER 
FIG.  42. 


der  at  equal  distances  along  the  axis.  The  center 
ring  is  split  into  two  equal  nearly  semicircular  arcs, 
the  gap  between  parts  being  about  J  inch.  The  rings 


Developement  of  Cylinder 
b  c 


Dotted  Lines  show  position  of  Brashes 
FIG.  43. 


are  connected  as  shown  in  the  development  of  the 
cylinder,  Fig.  43.  A  copper  brush  makes  contact 
with  each  of  the  outside  rings  and  a  pair  of  brushes 


218 


ELECTRIC   POWER  CONDUCTORS 


1 80°  apart  make  contact  with  the  two  halves  of 
the  split  ring.  The  cylinder  makes  one  revolution 
in  ten  seconds,  this  being  therefore  the  period  of  a 
complete  reversal  or  cycle. 

The  current  reverser  is  connected  to  the  generator 
and  cable,  as  shown  in  the  diagram,  Fig.  44. 

The  generator,  before  commencing  a  test,  is  short- 
circuited  through  a  knife  switch.  When  the  cable 

Generator 


Ammeter 


Commutating  Device 

Tabl 


Voltmeter 


Fault 


FIG.  44. 

is  connected,  the  switch  is  opened  and  the  machine 
allowed  to  build  up.  The  automatic  features  of  the 
machine  keep  the  current  down  to  less  than  10 
amperes,  the  voltage  rising  in  proportion  to  the 
resistance  of  the  fault. 

The  detectors  used  outside  are  of  two  kinds,  a 
compass  and  a  "  listening  coil."  The  compass  is 
used  wherever  possible  by  laying  it  on  the  cable  sheath 
and  looking  for  a  periodic  swing.  Where  live  D.  C. 


TESTING  <OF   WIRES   AND  CABLES          219 

feeders  are  close  by,  the  compass  needle  is  too  much 
disturbed  to  be  reliable,  and  a  "  listening  coil,"  con- 
sisting of  a  loop  of  wire  connected  to  a  telephone 
receiver,  is  used  instead. 

When  a  cable  breaks  down  it  is  tested  both  by  the 
Varley  loop  method  and  by  the  above  described 
method. 

The  use  of  a  mercury  arc  rectifier  instead  of  the 
arc  generator  has  been  suggested  and  promises  satis- 
factory results. 


CHAPTER  VIII 
INSTALLATION  OF  CABLES 

i.  INSTALLATION   OF  UNDERGROUND   CABLES 

THE  duct  having  been  rodded  and  wired,  is  ready 
at  any  time  to  receive  a  cable.  When  this  is  to  be 
done,  a  drawing  rope,  usually  a  Manila  rope  of  from 
}  inch  to  ij  inches  in  diameter,  is  attached  to  the 
wire  and  the  wire  pulled  at  the  opposite  end  until 
the  rope  is  pulled  in,. leaving  sufficient  slack  at  each 
end. 

The  cable  reel  is  placed  on  the  ground  near  the 
manhole  over  the  duct  into  which  the  cable  is  to  be 
pulled  and  in  such  a  position  that  the  cable  by  a  slight 
straightening  will  unwind  from  the  top  of  the  reel 
into  the  manhole  and  thence  into  the  duct.  The 
free  end  of  the  cable  must  first  be  fastened  in  some 
way  to  the  draw  rope. 

i.  It  is  usual  to  grip  the  cable  by  means  of  a  pair 
of  iron  wires  wound  around  it,  as  shown  in  Fig.  45, 
the  end  loops  being  hooked  to  the  pulling  rope. 
Ready-made  woven  wire  cable  grips  are  now  largely 
used.  These  grips  consist  of  loosely  woven  wires, 

220 


INSTALLATION   OF  CABLES  221 

and  are  placed  over  the  end  of  the  cable.  When 
stretched  longitudinally  they  shrink  laterally  round 
the  cable  and  grip  it  firmly  in  the  same  way  as  the 
improvised  grip  above  described.  As  the  wires  are 
liable  to  cut  into  the  lead  sheath  and  pull  it  off,  it 
is  not  unusual  with  large  rubber  and  cambric  cables 
to  bare  the  conductors  and  fasten  the  pulling  rope 
to  them,  thus  relieving  the  sheath  of  the  severe 
tension  caused  by  the  wires.  This,  however,  should 
never  be  done  if  there  is  any  moisture  in  the  ducts, 
as  water  is  liable  to  get  into  the  cable. 


TIG.  45. 

2.  Cables  may  be  pulled  in  any  one  of  three  ways: 

(a)  Direct  pulling  by  a  gang  of  men   at  the  rope. 
This  is  used  only  for. small  cables  or  very  short  lengths. 

(b)  Pulling    by    block    and    tackle.     This    is    the 
process  most  commonly  used,   although  difficult  for 
large  cables. 

(c)  Pulling  by  capstan  or  winch.     This  process  is 
only  used  for  long  sections  of  large  cable.     The  winch 
or    capstan    is    sometimes    operated    by    gasoline    or 
electricity,    but    such    devices    have    not    been    uni- 
versally successful  and  are  not  economical  unless  a 
large  amount  of  cable  pulling  is  to  be  done. 

When   pulling  is   done  by  block   and   tackle,    the 
pulling  rope  must  be  successively  gripped  at  points 


222  ELECTRIC   POWER  CONDUCTORS 

nearer  the  cable  as  the  cable  is  pulled  along;  it  is 
therefore  necessary  to  attach  it  to  the  pulling  device 
in  a  simple  way  and  so  that  it  can  be  readily  removed. 

Such  a  way  is  shown  in  Fig.  46,  in  which  it  will  be 
noted  that  the  upper  part  of  the  rope  presses  upon 
the  under  part  B  when  the  cable  is  pulled,  thus  hold- 
ing it  fast,  in  spite  of  the  absence  of  knots  or  other 
permanent  fastenings. 

When  the  cable  has  been  pulled  as  far  as  the  tackle 
will  permit,  the  rope  is  loosened,  the  tackle  pulled 
back  and  the  hook  attached  to  a  new  part  of  the 


FIG.  46. 

pulling  rope.  This  process  is  repeated  until  the 
cable  is  in  place. 

A  capstan  device  fitting  in  a  splicing  chamber  is 
shown  in  Fig.  47  and  the  method  of  using  the 
rope,  in  Fig.  48,  the  end  of  the  rope  which  reels  off, 
being  held  tight  against  the  drum  by  hand  and  the 
slack  allowed  to  coil  up. 

Street  capstans  are  also  used,  but  the  difficulty  of 
fastening  them  securely  is  a  serious  objection  to 
their  use. 

Before  pulling  cable  the  edges  of  the  duct  should 


INSTALLATION   OF  CABLES 


223 


be  covered  with  a  piece  of  lead,  such  as  a  piece  of 
scrap  cable  sheathing,  in  order  to  protect  the  cable 
from  abrasion  during  drawing.  A  man  should  be 
stationed  in  the  chamber  to  superintend  the  feeding-in 


FIG.  47- 

of  the  cable,  taking  care  that  it  runs  tangentially 
into  the  duct  without  injury  to  its  surface.  In  the 
event  of  the  feeding-in  not  progressing  properly,  this 
man  should  notify  the  men  above  to  signal  the  pullers 
to  stop  or  proceed  with  caution.  There  should  also 
be  a  man  in  the  chamber  at  the  pulling  end  to  notify 


224 


ELECTRIC   POWER  CONDUCTORS 


the  pullers  of  anything  amiss  and  to  signal  stop  when 
the  cable  has  been  pulled  sufficiently.  When  a  chamber 
capstan  is  used,  it  is  often  necessary  to  move  the 
draw  rope  from  the  end  of  the  cable  grip  to  a  point 
at  the  side  of  the  cable  in  order  to  pull  the  cable  end 
beyond  the  capstan,  so  that  it  will  not  be  necessary 
to  use  the  part  injured  by  the  grip. 


Pulling  Cable     \\\.  •>  >  .  //// 


Held  taut 


MIL 


FIG.  48. 


2.  INSTALLATION  OF  OVERHEAD  WIRES 

The  erection  of  overhead  wires  is  performed  in 
various  ways,  depending  upon  local  conditions  and 
upon  the  preferences  of  the  engineer.  There  are, 
however,  two  entirely  different  styles  of  construc- 
tion to  be  considered,  namely,  the  simple  span  and 
the  messenger  wire. 

The  former  is  used  where  the  conductors  have 
sufficient  tensile  strength  to  support  the  stresses  due 
to  their  own  weight  and  the  weight  of  wind  and  ice  ; 
the  latter  is  used  where  the  conductors  are  unable  to 
support  these  stresses,  as,  for  example,  in  the  case  of 
insulated  cables. 


INSTALLATION   OF  CABLES  225 

Simple  Spans.  Starting  at  an  anchored  pole,  a  rope 
is  placed  over  the  cross  arm  and  the  wire  pulled  over 
the  latter  and  drawn  to  the  next  pole,  where  it  is 
again  pulled  up  by  means  of  the  rope  and  so  drawn 
along  from  pole  to  pole  until  the  reel,  which  remains 
at  the  starting  point,  is  exhausted.  The  pulling  may 
be  done  by  a  gang  of  men,  by  horses,  or  by  a  loco- 
motive if  the  pole  line  parallels  a  railroad.  Care 
must  be  taken,  as  the  end  of  the  reel  is  approached, 
that  the  wire  does  not  slip  away  and  fall  over  the 
first  pole. 

The  next  step  is  to  place  the  cable  on  the  insulators. 
This  may  be  accomplished  by  means  of  a  block  and 
tackle  if  there  is  a  cross  arm  above,  but  unless  the 
wire  is  very  large  there  is  no  difficulty  in  doing  it  by 
hand.  Where  the  cable  is  very  heavy  and  there 
is  no  cross  arm  above,  the  best  procedure  is  to  rig 
up  a  temporary  cross  arm  or  boom  projecting  from 
the  pole. 

The  wire,  being  set  upon  the  insulators,  must  be 
drawn  up  to  the  required  tension.  Starting  at  the 
first  pole  after  the  anchorage,  the  wire  is  gripped 
by  a  clamp  attached  to  a  rope  and  the  rope  pulled 
until  the  wire  is  drawn  up  to  the  required  sag.  The 
wire  is  then  firmly  attached  to  the  insulator  and 
the  process  repeated  at  the  other  poles. 

The  foreman  should  be  provided  with  a  table  or 
curve  showing  the  proper  sag  at  different  tem- 
peratures and  spans.  The  desired  sag  is  obtained 


226 


ELECTRIC   POWER  CONDUCTORS 


by  sighting  from  pole  to  pole  by  means  of  devices 
attached  to  the  cross  arm  or  wire,  the  wire  being 
drawn  up  until  the  point  of  lowest  sag  is  tangential 
to  the  sight  line. 

Messenger  Construction.  The  messenger  wire,  usu- 
ally a  steel  cable,  having  been  erected  as  described 
above,  a  "  leading-up "  wire  is 
stretched  from  an  anchorage  to  the 
messenger  wire  on  the  starting  pole. 
A  rope  is  fastened  to  the  end  of 
the  cable  to  be  suspended  and 
carried  along  the  messenger  wire 
over  the  first  two  poles.  The  cable 
is  then  slowly  drawn  up  the  inclined 
wire,  under  the  cross  arm,  and  along 
the  messenger  wire,  carriers  being 
attached  to  the  cable  as  it  is  paid 
out  from  the  reel.  Men  stationed 
on  each  pole  remove  the  carriers 
from  the  messenger,  pass  them  under 
the  cross  arm,  and  replace  them  on  the  other  side. 
The  cable  is  pulled  along,  in  this  way,  until  the  reel 
is  exhausted.  A  common  type  of  carrier  for  this 
purpose  is  shown  in  Fig.  49,  but  wire  hooks  are  some- 
times used  instead. 

When  the  whole  length  of  cable  is  suspended,  a  lineman 
rides  along  the  messenger  wire  in  a ' '  carriage  ' '  or  trolley- 
seat,  and  replaces  the  carriers  by  permanent  clips 
which  firmly  fasten  the  cable  to  the  messenger  wire. 


FIG.  49. 


INSTALLATION  OF   CABLES  227 

3.  SPLICING 
JOINING  BARE  WIRES 

Copper.  Solid  wires  up  to  No.  oo  B. 
and  S.  are  almost  invariably  joined  by 
the  Western  Union  method.  To  make 
such  a  joint,  bring  the  two  ends  of  the 
wire  together  so  that  they  lap  from  3  to 
8  ins.  Then  beginning  midway  between 
the  two  ends  wind  each  overlapping  end 
spirally  around  the  adjacent  wire,  as 
illustrated  in  Fig.  50.  With  hard  drawn 
copper  it  is  important  to  avoid  giving 
the  wire  too  much  twist.  This  is  ac- 
complished by  making  the  first  turn  at 
a  small  angle  and  then  gradually  bring- 
ing successive  turns  nearer  to  a  right 
angle  until  they  form  a  close  spiral. 

Cables  are  generally  joined  by  un- 
stranding  them  for  three  or  four  feet, 
dovetailing  the  wires  together  and  wrap- 
ping them  one  by  one  round  the  unopened 
part  of  the  cable.  Solder  should  not 
be  used  on  overhead  wires  lest  the  tensile 
strength  be  reduced  by  overheating. 

Numerous  mechanical  connectors  have 
met  with  varying  success,  but  do  not 
enjoy  the  vogue  of  the  ordinary  line 
splice  described  above. 


228  ELECTRIC   POWER  CONDUCTORS 

Aluminum.  Aluminum  cables  are  joined  mechani- 
cally without  the  use  of  solder. 

Splices  between  wires  of  an  area  equal  to  No.  oooo 
B.  and  S.  gauge,  or  anything  smaller,  are  best  made 
by  twisting.  The  two  ends  to  be  joined  are  inserted, 
side  by  side,  into  a  piece  of  flattened  aluminum  tubing, 
after  which  the  ends  of  the  tubing  are  gripped  by  a 
pair  of  connectors  having  a  groove  of  the  same 
shape  as  the  tube,  and  from  two  and  one-half  to  four 
complete  twists  given  to  the  tube  with  its  contained 
wires. 

Larger  conductors  than  No.  oooo  B.  and  S.  may 
be  joined  by  special  connectors  supplied  by  the 
cable  manufacturers  or  firms  dealing  in  such  special- 
ties. A  representative  joint  of  this  type  is  made 
by  inserting  the  ends  of  the  cable  into  a  cast  aluminum 
sleeve.  The  sleeve  is  then  inserted  between  dies 
in  a  hydraulic  jack  and  pressure  applied  to  the  dies 
until  the  metal  of  the  sleeve  and  of  the  cable  flow 
together  into  a  solid  homogeneous  mass.  A  modified 
form  of  this  joint  has  the  sleeve  made  in  two  parts, 
which  are  pressed  on  the  cable  at  the  factory.  These 
terminals  are  provided  with  internally  threaded  ends, 
one  right-handed  and  the  other  left-handed,  and 
cables  are  joined  by  screwing  a  right-  and  left-hand 
threaded  stud  into  the  terminals.  Such  joints,  how- 
ever, are  not  as  popular  as  the  ordinary  cable  splice, 
which  is  made  by  unstranding  the  cable  for  three 
or  four  feet,  dovetailing  the  wires  together  and 


INSTALLATION  OF  CABLES  229 

wrapping  them  one  at  a   time  round  the   unopened 
part  of  the  cable. 


JOINING  INSULATED  CABLES 

Preliminary.  (i)  Inspect  cable  from  edge  of  duct 
to  end,  looking  for  mechanical  injury. 

(2)  Be  certain  to  select  the  corresponding  incom- 
ing and  outgoing  sections. 

(3)  Place  bushings  in  the  mouths  of  ducts. 

(4)  Bend  cables  neatly,  taking  care  to  avoid  sharp 
curves,  until  the  ends  meet  properly  at  the  point  of 
designated  for  the  joint.     The  completed  joint  should 
lie  between  supports  in  such  a  way  that  there  will 
be  no  strain  on  the  joint  itself.     In  single  conductor 
cables,  where  a  butt  joint  is  used,  the  cables  should 
overlap    very    slightly,    but    in    multiple    conductor 
cables,  where  the  wire  joints  must  be  staggered,  the 
cables   should   overlap   sufficiently   to   allow   for   the 
proper  distribution  of  wire  splices. 

Drying  Ends  of  Cable.  The  ends  of  the  cable  should 
be  carefully  examined  for  moisture,  and  if  any  is 
discovered,  the  cable  should  be  cut  back  until  all 
evidence  of  moisture  disappears,  care  being  taken 
not  to  cut  back  so  far  as  to  render  it  too  short  to 
make  the  joint.  If  moisture  is  still  evident,  apply 
heat  to  the  lead  cover  of  the  cable,  beginning  near 
the  duct  and  very  slowly  approaching  the  open  end. 
This  heating  may  be  effected  either  by  pouring  on 


230  ELECTRIC   POWER  CONDUCTORS 

very  hot  insulating  compound  and  catching  it  in  a 
vessel  held  underneath,  or  by  means  of  a  gasoline 
torch.  If  the  dryness  of  the  cable  remains  doubtful, 
an  insulation  test  should  be  made  before  jointing, 
and  if  the  insulation  is  abnormally  low,  the  cable 
section  should  be  replaced.  Never  cut  off  the  end  of 
one  section  until  sure  there  is  no  moisture  in  the 
other  section,  as  it  may  be  possible  to  change  the 
location  of  the  splice  in  case  the  other  end  is  defective. 
Removing  the  Lead,  (i)  Mark  the  lead  at  the  point 
it  is  to  be  removed  and  make  a  deep  cut  around  the 
sheath,  gradually  increasing  the  depth  of  the  cut 
until  the  lead  is  cut  through,  taking  care  not  to 
cut  the  insulation  in  the  slightest  degree.  A  chip- 
ping knife  and1  hammer  or  a  special  tool  may  be  used 
for  this  purpose. 

(2)  Cut  the  lead  lengthwise  from  the  circular  cut 
to  the  end,  taking  the  precaution  to  hold  the  knife 
tangent  to  the  insulation  so  that  it  will  pass  between 
the  insulation  and  the  sheath. 

(3)  Pull  off  the  lead  with  a  pair  of  pliers. 

(4)  When  the  lead  is  removed  examine  all  parts  of 
the  bared  insulation  and  remove  all  loose  and  pre- 
jecting  particles  of  lead,  especially  at  the  edge  of  the 
circular  cut. 

Preparing  Cable  Sleeves.  (i)  Scrape  the  ends  of 
the  sleeve  for  a  length  of  about  2  inches  along  the 
outside,  using  a  knife  or  a  shave-hook  and  smear  the 
cleaned  surfaces  with  tallow. 


INSTALLATION   OF  CABLES  231 

(2)  Slip  the  sleeve  over  the  more  convenient  end 
of  the  cable  and  push  it  out  of  the  way. 

Removing  Insulation.  Cut  back  the  insulation  of 
each  section  for  a  length  equal  to  half  the  length  of 
the  connector  plus  from  J  to  J  inch,  depending  on 
the  size  of  the  cable. 

With  multiple  conductor  cables  having  an  outer 
insulating  belt  it  is  necessary  to  cut  the  outer  insu- 
lation further  back  than  the  inner  insulation.  In 
doing  this  is  it  essential  to  avoid  cutting  the  inner 
insulation  in  the  slightest  degree. 

Tinning  the  Copper.  Pour  molten  solder  over  the 
copper,  using  a  tallow  candle  as  flux. 

Joining  Copper  by  a  Connector.  The  usual  way  to 
join  the  cable  ends  is  to  use  a  copper  sleeve,  having 
a  cross-sectional  area  at  least  equal  to  that  of  the 
cable  itself.  This  condition  is  obtained  by  making 
the  outside  diameter  of  the  connector  about  ij  times 
that  of  the  wire. 

The  usual  length  of  sleeve  is  shown  in  Table  II 
below : 

(1)  Put  the  connector  over  one  cable  end  and  then 
slip  the  other  cable  end   in  until  the  two    ends   butt 
in  the  center  of  the  connector. 

(2)  Sweat  on  the  connector  by  pouring  on  solder 
from  a  ladle,   catching  the  surplus  solder  in  a  pot 
below. 

(3)  When  thoroughly  saturated  with  molten  solder, 
wipe  the  joint  with  a  wiping  cloth,  taking  care  to 


232 


ELECTRIC   POWER  CONDUCTORS 


leave  no  projecting  points  or  sharp  edges.  This  is 
extremely  important  in  high-tension  cables,  as  sharp 
points  or  edges  greatly  increase  the  dielectric  stress 

TABLE  I 

DATA  ABOUT  CABLE  SLEEVES 
(Standard  Underground  Cable  Co.) 


Outside 
Diameter 
of  Cable, 
Mils. 

Inside 
Diameter 
of  Sleeve, 
Inches. 

Length  of 
Sleeve, 
Inches. 

Gallons  of 
Compound 
per 
Joint. 

Wiping 
Solder  per 
Joint, 
Lbs. 

Single     Con- 

Up to  550 

I 

8 

0.05 

0.9 

ductor,    light 

551-950 

x| 

10 

O.I 

1-7 

and      power, 

95I-i35° 

2 

12 

O.2 

2.8 

up    to    6600 

1351-1750 

»i 

12 

o-3 

4-2 

volts 

1751-2150 

3 

14 

o-5 

5-5 

2151-2550 

si 

14 

0.6 

6.8 

Single      con- 

Up to  550 

i 

10 

0.05 

0.9 

ductor,    light 

55i-  95° 

'*i 

12 

O.I 

i-7 

and      power, 

95I-I35° 

2 

14 

0.2 

2.8 

above      6600 

1351-1750 

2* 

16 

0.4 

4-2 

volts 

1751-2150 

3 

18 

0.6 

5-5 

2151-2550 

3i 

18 

0.8 

6.8 

Multicon- 

Up  to  800 

*i 

14 

O.2 

i-5 

ductor,    light 

801-1200 

2 

16 

0.25 

2-5 

and     power, 

1201-1600 

*i 

16 

o-35 

3-7 

all  voltages 

1601-2000 

3 

18 

0.6 

5-o 

2001-2400 

3i 

18 

0.8 

6-3 

2401-2800 

4 

18 

I.O 

7-6 

2801-3200 

4l 

20 

1.4 

8-3 

Joining   Copper  without   a   Connector.       (i)   Cut    the 

wires  alternately  short  and  long,  so  that  when  the 
two  ends  are  butted,  the  long  wires  of  one  cable 
will  fit  against  the  shortened  wires  of  the  other  cable 
and  the  two  cables  will  be  interlaced. 


INSTALLATION   OF  CABLES 


233 


TABLE  II 

SIZE  OF  COPPER  CONNECTORS 


Size  of  Cable. 

Length  of 
Connector. 

o  B.  &  S.  to  ooo  B.  &  S. 
oooo  B.  &  S.  to  1,000,000  c.m. 
1,250,000  to  2,000,000  c.m. 

i    in.  to  2  in. 
2^  in.  to  4  in. 
5    in.  to  6  in. 

(2)  Bind  the  joint  with  binding  wire. 

(3)  Sweat  the  cables  together  by  pouring  on  molten 
solder. 

This  type  of  joint  is  superior  to  the  connector 
joint  for  cables  larger  than,  say,  one-half  million  c.m., 
because  there  is  less  danger  of  the  cables  being  pulled 
apart. 

Insulating  the  Joint  with  Tape,  (i)  If  the  cable  in- 
sulation is  thicker  than  the  connector,  taper  it  grad- 
ually with  a  sharp  knife. 

(2)  Then   wind   on    insulating   tape    of    the   same 
material    as    the   cable    insulation    until    a    thickness 
somewhat  greater   than  that  of  the  cable  insulation 
is  obtained.     The  tape  should  be  wound  tightly  and 
evenly,   running   up   the   tapered   part   of   the   cable 
insulation  until  well  attached  to  it. 

(3)  "Boil   out  "    the   insulation   by   pouring   over 
it    hot    compound.     The    compound    should    be    hot 
enough  to  throw  off  moisture  readily  without  being 
hot  enough  to  ignite  a  piece  of  paper  dipped  into 
it.     The    surplus    compound    should    be    caught    in 
a  pan,  and  when  heated  may  be  used  again. 


234  ELECTRIC   POWER  CONDUCTORS 

The  jointer  should  not  take  a  pot  of  insulation 
into  a  splicing  chamber  until  he  has  taken  off  the 
lid  and  assured  himself  that  it  is  at  the  proper  tem- 
perature. Many  accidents  to  men  and  cables  are 
caused  by  neglect  of  this  precaution. 

Insulating  the  Joint  with  Sleeves.  Instead  of 
winding  on  insulating  tape,  an  insulating  sleeve  may 
be  slipped  over  the  wires  before  soldering  and  put 
in  place  when  the  wires  are  joined.  The  internal 
diameter  of  the  sleeve  must  be  great  enough  to 
permit  it  to  slip  easily  over  the  insulation. 

(1)  After  the  wires  are  joined,  wind  cotton  tape 
tightly  over  them  until  entirely  covered  up  to  the 
level  of  the  original  insulation. 

(2)  Slip  the  insulating  tube  over  the  taped  joint 
and  fasten  it  in  place  with  a  layer  of  cotton  tape. 

(3)  "  Boil  out  "  the  joint  by  pouring  on  insulation. 
With  multiple  conductor  cables  having  an  outside 

belt  it  is  necessary  to  slip  a  large  tube  over  the  belt 
before  splicing  the  wires. 

Tubes  may  be  of  prepared  paper,  varnished  cloth, 
or  micanite. 

Wiping  on  the  Sleeve.  (i)  Bring  the  lead 
sleeve  into  position  so  as  to  extend  equally  over 
the  lead  on  each  cable  end,  and  dress  down  the  ends 
close  to  the  lead  of  the  cable,  taking  care  to  make 
the  sleeve  concentric  with  the  cable. 

(2)  Join  the  sleeve  and  sheath  by  means  of  a 
wiped  solder  joint.  That  is  to  say,  solder  is  poured 


INSTALLATION   OF  CABLES 


235 


on  with  a  ladle  and  as  quickly  wiped  with  a  cloth. 
This  is  continued  until  an  absolute  air-tight  joint 
is  obtained.  The  joint  should  be  carefully  inspected, 
a  small  mirror  being  used  to  examine  the  under 


ffl 


FIG.  51. 

side,  and  if  any  roughness  or  weakness  is  dis- 
covered, should  be  worked  over.  A  small  blow- 
hole undetected  at  this  stage  will  give  great  trouble 
later. 


236  ELECTRIC   POWER  CONDUCTORS 

Filling  the  Sleeve.  (i)  When  the  sleeve  is 
well  wiped  on,  make  two  small  holes  in  the  top  of 
the  sleeve  and  pour  hot  insulation  in  one  hole  until 
it  appears  at  the  other,  and  then  in  each  hole  alter- 
nately until  the  sleeve  is  filled.  If  any  frothing 
appears  on  the  insulation,  continue  pouring  it  in 
one  hole  while  it  escapes  out  the  other,  until  the 
frothing  stops. 

(2)  Leave  the  joint  to  cool  for  say  an  hour,  and 
then  add  compound  to  compensate  for  settling 

(3)  Put  a  small  piece  of  lead  over  the  holes  and 
solder  it  on. 

(4)  Allow  the  joint  to  thoroughly  cool  and  solidify 
and  then  put  it  in  its  permanent  place. 

The  following  compounds  are  used  for  filling 
sleeves. 

Paraffin  wax; 

Ozite ; 

G.  E.  Co.  No.  67  compound; 

Voltax,  etc. 

Key  to   Fig.   51.      The  various  stages  for  a  typical 

joint  in  a  single  conductor  cable  are  shown  in  Fig.  5 1 . 

I    shows  the  lead  stripped  and  the  wires  ready 

to  be  joined. 
II    shows  the  wires  joined  by  a  copper  connector. 

III  shows    the    insulation    tapered    to    receive    the 

tape. 

IV  shows  the  joint  insulated  with  tape. 


INSTALLATION   OF  CABLES  237 

V   shows  the  lead  sleeve  slipped  in  position. 
VI   shows  the  ends  of  the  lead  sleeve  hammered 

down  preparatory  to  wiping. 
VII    shows  the  lead  sleeve  wiped  on. 
VIII   shows  the  lead  sleeve  filled  and  the  holes  in 
it  closed  by  a  sheet  of  lead. 


CHAPTER  IX 
DEPRECIATION  AND  DETERIORATION 


i.  DEPRECIATION 

DEPRECIATION   is   a    "  lessening   of   value "    which 
may  be  brought  about  by  the  following  causes. 

1.  Deterioration  due  to  the  ravages  of  time  and 
the  effects  of  the  elements. 

2.  Wear  and  tear  incident  to  use. 

3.  Displacement    by    reason    of    obsolescence    or 
supersession,    resulting    from    developments    of    the 
art. 

The  natural  life  of  cables  in  ducts  is  estimated  by 
R.  Hammond  as  thirty  years. 

Value  of  a  Cable  after  Installation.    Calling  the  original 
cost  100,  let 

y  =  value   of   cable   immediately   after   installation 
expressed  as  percentage  of  the  original  cost. 
L  =  life  of  cable,  years ; 
5  =  scrap  value  at  end  of  L,  years,  expressed  as  per 

cent  of  original  cost; 

oc=  value  after  being  installed  y  years,  expressed  as 
per  cent  of  original  cost.     Then  if  the  cable  is 

238 


DEPRECIATION   AND   DETERIORATION      239 

assumed  to  depreciate  by  a  constant  amount 
every  year, 

,,     v-s 


If,  however,  the  cable  is  assumed  to  depreciate  at  a 
constant  rate  per  annum, 

V  is  less  than  the  original  cost  for  the  following 
reasons : 

(1)  Price  at  which  cable  was   bought  may  be  arti- 
ficially controlled  so  as  to  be  above  a  free  market  price. 

(2)  The  cable  lengths  will  probably  be  unsuitable 
for  other  installations  and  will  have  to  be  reduced, 
thereby  wasting  some  cable. 

(3)  Cable  is  injured  to  some  extent  during  instal- 
lation. 

It  is  important  to  distinguish  between  the  value  of 
a  cable  if  removed  and  its  value  as  an  integral  part 
of  a  transmission  system,  this  latter  depending  upon 
its  efficacy  as  a  revenue  producer  as  well  as  upon  its 
cost  and  age. 

Life  and  Depreciation.  Equipment  worth  p  per 
cent  of  its  original  cost  after  y  years,  is  said  to 
depreciate  at  the  rate  of  P  per  cent,  where 

D     (loo-p) 


240  ELECTRIC   POWER  CONDUCTORS 

If   C  =  original   cost,   depreciation   is   offset   by  an 

pC 

annuity   to   redeem    £  —   in   y  years. 
100 

Depreciation  Calculations.  The  effects  of  deprecia- 
tion may  be  offset  by  putting  aside  a  depreciation  fund 
which,  added  to  the  scrap  value  of  the  old  cables,  will 
enable  new  ones  to  be  purchased. 

The  payment  p  to  be  made  at  the  end  of  each 
year,  in  order  to  possess  the  sum  5  at  the  end  of  n 
years,  is  as  follows. 


The  payment  p  to  be  made  at  the  beginning  of 
each  year,  in  order  to  possess  the  sum  5  at  the  end 
of  n  years,  is  as  follows: 

r 


2.     DETERIORATION    BY   ELECTROLYSIS    AND   MIS- 
CELLANEOUS CAUSES 

Principles  of  Electrolysis  Protection.  Where  a 
current  passes  through  an  electrolyte,  the  latter  is 
decomposed,  hydrogen,  metals,  and  alkaline  bases 
appearing  at  the  cathode  or  negative  electrode  and 
oxygen  and  acids  at  the  anode  or  positive  electrode. 
In  other  words,  the  corrosive  agents,  oxygen  and 
acids,  travel  against  the  current,  and  it  is  therefore 
only  at  the  anodes  or  places  where  the  current 


DEPRECIATION    AND   DETERIORATION      241 

leaves  the  metal  to  enter  the  electrolyte  that  the 
electrolytic  corrosion  occurs. 

The.  important  condition  for  electrolysis  preven- 
tion is  therefore  to  keep  current  from  flowing  from 
any  underground  metal  work  to  earth  or  water  in 
contact  with  it.  The  current  flowing  from  the  under- 
ground metal  work  can  be  kept  a  minimum  in  three 
ways  in  grounded  return  railway  systems. 

First.  Keeping  the  potential  difference  between 
metal  and  ground  very  low,  or  in  other  words,  by 
keeping  down  the  drop  in  the  grounded  return 
circuit. 

(a)  By  thorough  bonding. 

(b)  By  frequent  cross   bonding  between  tracks. 

(c)  By  using  negative  feeders  to  reduce  the  drop 
in  the  grounded  system. 

(d)  By    using    insulated    negative    feeders    taking 
current  from  the  rails  at  numerous  points. 

(e)  By  negative  boosters  on  the  track  rails. 
Second.    Keeping  the  metal  electronegative  to  the 

earth. 

(a)  By  connecting  to  the  station  negative  bus. 

(b)  By   means   of   negative   boosters   connected   to 
the  metal  work. 

Third.  Insulating  the  metal  work. 

(a)  In  concrete. 

(b)  By  paint. 

Those  methods  requiring  special  comment  are  more 
fully  described  below. 


242  ELECTRIC   POWER  CONDUCTORS 

Insulated  Negatives.  The  drop  in  the  grounded  rails 
may  be  diminished  by  taking  the  current  off  by 
numerous  insulated  cables  connected  to  the  track  rails. 
The  drop  in  these  cables  may  be  of  any  magnitude 
without  affecting  electrolytic  conditions.  This  system 
is  in  use  in  the  New  York  subways. 

Negative  Boosters  Connected  to  Tracks.  This  subject 
is  treated  under  negative  boosters. 

Connecting  Metal  to  Station  Bus.  Pipes,  columns,  etc., 
connected  by  an  insulated  cable  to  the  negative  bus 
are  immune  from  electrolysis.  This  method  of  pro- 
tection is  especially  applicable  in  connection  with  the 
insulated  feeder  system  described  above,  as  where 
that  is  used  the  main  insulated  negative  feeders  are 
available  for  this  purpose  and  special  grounding 
cables  are  unnecessary. 

Negative  Boosters  connected  to  Metal.  Important 
iron  work,  such  as  iron  tunnels  and  pipes  under  water, 
may  be  protected  from  electrolysis  by  using  a  booster 
to  render  them  negative  to  the  surrounding  water. 
Such  boosters  are  usually  motor  driven,  and  have 
their  negative  terminal  connected  at  intervals  to  the 
iron  work.  The  positive  terminal  should  be  con- 
nected to  a  cable  paralleling  the  tunnel  and  con- 
nected at  intervals  to  graphite  anodes.  Where 
conditions  permit,  a  single  anode  may  be  sufficiently 
effective.  The  voltage  must  be  sufficient  to  supply 
a  slight  current  after  polarization  has  been  estab- 
lished 


DEPREQI^TION   AND   DETERIORATION      243, 

Electrolysis  of  Concrete  Encased  Steel.  Concrete  being 
porous,  when  saturated  with  water  permits  the 
passage  of  current.  Hence  if  a  current  is  estab- 
lished through  concrete  electrolysis  can  take  place 
through  it. 

There  is,  however,  a  marked  increase  of  resistance 
following  the  application  of  current  and  consequent 
tendency  of  the  corrosive  action  to  cease.  This 
increase  of  resistance  may  be  from  ten  to  fifteen  fold 
before  it  becomes  constant. 

Insulation  of  Metal  Work  by  Paint  and  Asphalt.  Metal 
work  perfectly  covered  with  non-conducting  paint  is 
impervious  to  electrolytic  corrosion.  Unfortunately 
a  slight  flaw  in  the  paint  will  often  suffice  to  start 
trouble.  Several  coats  of  paint  ajre  therefore  essential 
for  proper  protection.  Asphalt  paint  and  others  of 
similar  nature  are  generally  used  as  common  paints 
are  acted  upon  by  the  damp  ground  especially  if 
alkalis  are  present. 

Alternating-Current  Electrolysis.  (].  L.  R.  Hayden, 
Proc.  Am.  Inst.  Elec.  Eng.,  1907.)  Alternating  cur- 
rent electrolysis  is  not  a  phenomenon  like  direct 
current  electrolysis  on  which  quantitative  general 
laws  can  be  formulated;  but  it  is  of  the  character  of 
a  secondary  effect;  that  is,  the  action  of  the  positive 
half  wave  is  not  quite  reversed  by  the  action  of  the 
negative  half  wave  leaving  a  small  difference  rarely 
exceeding  J%  of  the  electrolytic  action  of  an  equal 
direct  current. 


244  ELECTRIC   POWER  CONDUCTORS 

A  direct  current  about  1.5%  of  the  alternating 
current  is  a  perfect  protection  against  2  5 -cycle  cur- 
rent. The  corrosion  increases  with  decrease  of  fre- 
quency. 

Deterioration  from  Miscellaneous  Causes.  Cable  sheaths 
are  generally  somewhat  injured,  during  installation, 
by  projecting  points  on  the  surface  of  the  ducts. 
When  it  is  remembered  that  a  great  length  of  cable 
is  pulled  over  each  projection  of  this  sort,  the  possible, 
extent  of  the  damage  is  seen  to  be  very  great  and  the 
importance  of  thorough  and  conscientious  examina- 
tion of  ducts  realized.  Duct  inspection  is  often 
performed  by  incompetent  people  or  in  a  perfunctory 
manner,  which  is  encouraged  by  duct  manufacturers. 
This  arises  from  the  fact  that  the  process  of  glazing 
usually  develops  a  very  high  percentage  of  defective 
ducts  which  the  manufacturer  is  anxious  to  dispose 
of,  bids  being  usually  made  on  the  assumption  that 
the  customer  will  be  lenient  in  the  inspection.  Engi- 
neers should  remember  that  electrolysis  is  a  gentle 
agency  of  destruction  compared  with  the  ripping 
action  of  a  projection  in  a  duct. 

In  warm  climates,  lead  sheathing  is  attacked  by 
beetles,  caterpillars,  and  even  wasps.  The  Home 
Telephone  Co.  of  Santa  Barbara,  CaL,  has  been 
troubled  by  insect  holes  of  an  eighth  of  an  inch 
diameter  in  their  cable  sheaths. 


CHAPTER  X 
THIRD-RAIL  CIRCUITS 

The  design  of  railway  feeders  is  so  much  influenced 
by  the  systems  of  contact  conductors  to  which  they 
are  connected,  that  a  study  of  the  general  charac- 
teristics of  such  systems  constitutes  an  important 
phase  of  the  feeder  problem. 

The  first  principle  in  the  design  of  contact  con- 
ductor circuits  is  that,  when  the  contact  conductor 
becomes  grounded  on  account  of  any  kind  of  acci- 
dent, this  grounding  shall  not  be  the  cause  of  dan- 
gerous or  expensive  damage  of  any  kind.  Such 
damage  may  involve  material  on  the  right  of  way, 
rolling  stock,  feeder  conductors,  power  and  control 
equipment,  and  may  seriously  derange  the  schedule 
by  delaying  trains  on  one  or  more  tracks.  It  is  there- 
fore essential  to  sectionalize  the  third  rail  or  trolley 
wire  in  such  a  way  as  to  localize  this  damage  as 
much  as  possible.  One  way  of  doing  this  imme- 
diately suggests  itself,  namely,  the  use  of  auto- 
matic circuit  breakers  which  will  open  when  a  ground 

*  Abstracted  from  an  article  by  the  author  in  the  Electrical  World,  April 
22,  1905. 

245 


246  ELECTRIC   POWER  CONDUCTORS 

occurs.  This  method,  however,  is  not  as  simple 
as  it  seems,  for,  although  it  is  easy  to  get  a  circuit 
breaker  that  will  open  with  a  certain  current,  it 
is  impossible  to  get  one  that  has  the  power  of  dis- 
tinguishing between  a  ground  and  an  abnormal 
load.  This  is  the  principal  difficulty  encountered 
when  designing  a  system  of  third-rail  sectionalizing 
devices.  A  very  destructive  short  circuit  may  take 
even  less  current  than  a  normal  load,  and  it  will, 
therefore,  not  open  a  circuit  breaker  set  to  open  at  an 


Substation  .  Substation 

FlG.  52. — Third  Rails  not  Interconnected  but  Sectionalized. 

abnormal  current.  When,  however,  the  circuit 
breaker  does  open,  its  contacts  may  be  so  damaged 
that  it  cannot  be  put  back  in  circuit.  For  these 
reasons  it  is  obvious  that  the  promiscuous  use  of 
circuit  breakers  is  not  desirable,  and  that  none  should 
be  installed  without  a  very  thorough  consideration 
of  the  advantages  and  disadvantages  which  may 
arise  from  local  conditions  in  each  case. 

The  designer  of  a  sytem  of  third  rails  should 
remember  that  it  is  far  more  important  to  have  a 
reliable  system  of  connection  between  the  bus  and 
the  cars  than  the  most  complete  system  of  auto- 


THIRD-RAIL  CIRCUITS  247 

matic  or  other  interrupting  devices.  It  is  obvious 
that  whereas  the  interruption  of  current  is  an  inci- 
dental and  unusual  requirement,  certainty  of  supply 
is  the  requirement  of  fundamental  importance. 
Hence,  certainty  of  supply  must  riot  in  any  way  be 
sacrificed  to  certainty  of  non-interruption.  Judging 
from  some  complicated  and  expensive  systems  now  in 
use,  it  would  seem  that  this  fundamental  proposi- 
tion is  not  universally  appreciated.  One  corollary 
to  be  drawn  from  this  is  that  it  is  not  desirable  to 


Subitalion  Substation 

FIG.  53. — Third  Rails  Interconnected  but  not  Sectionalized. 

have  circuit-breakers  between  the  load  and  the 
source  of  current,  unless  they  are  under  constant 
supervision.  As  a  rule,  this  means  that  there  should 
be  no  circuit-breakers  in  series  with  the  line  except 
those  in  the  power  house  or  substation. 

It  is  desirable  that  an  accident  to  the  third  rail 
of  one  track  should  not  in  any  way  interfere  with 
the  traffic  on  the  other  tracks.  For  this  reason, 
each  track  should  be  separately  fed  from  the  bus 
without  any  other  connections.  Unfortunately  this 
system  of  separate  feeding  is  very  uneconomical,  as 
it  does  not  utilize  all  the  available  feeder  metal 


248  ELECTRIC   POWER  CONDUCTORS 

to  carry  the  current,  unless  all  the  tracks  are 
always  equally  loaded.  In  order  to  obtain  the 
advantages  of  separately  fed  tracks,  and  to  secure 
maximum  feeder  economy,  the  method  of  connecting 
together  all  the  tracks  through  circuit-breakers  im- 
mediately suggests  itself.  Damage  to  such  circuit 
breakers  is  not  liable  to  cause  serious  trouble,  as 
they  do  not  interrupt  the  current  along  each  third 
rail,  and  they  are  therefore  not  essential  in  the 
scheme  of  supply.  Whether  the  tracks  are  to  be 


Substation  •  Substation 

FIG.  54. — Third  Rails  Interconnected  and  Sectionalized. 

permanently  connected  or  connected  through  switches 
or  circuit-breakers,  or  not  connected  at  all,  will 
depend  upon  local  conditions  as  viewed  by  the  en- 
gineer. 

In  order  to  confine  the  effects  of  a  short-circuit 
to  a  limited  portion  of  the  track  on  which  it  occurs, 
it  is  desirable  to  divide  the  third  rail  into  a  number 
of  sections.  It  is,  however,  not  advantageous  to 
carry  this  division  very  far,  as  an  accident  at  any 
point  on  a  track  will  affect  the  traffic  a  long  way 
behind.  As  a  rule  it  is  sufficient  to  break  the  rail 
in  front  of  the  substations  and  at  cross-overs.  Breaks 


THIRD-RAIL  CIRCUITS  249 

at  cross-overs  are  essential  in  order  that  a  train 
may  go  around  a  dead  section  of  rail  by  crossing  to 
another  track.  Breaks  in  front  of  the  substations 
are  convenient  because  it  is  possible  to  break  the 
rail  there  without  having  to  install  switches  or  circuit- 
breakers  on  the  line.  Breaks  in  the  rail  at  cross- 
overs distant  from  the  substations  involve  the  use 
of  circuit -breakers  or  switches  to  interrupt  the  con- 
ductor which  joins  the  sections.  As  circuit-breakers 
in  series  with  the  line  are  undesirable,  it  only  remains 


FIG.  55. — Knife  Switches  at  Cross-overs. 

to  recommend  the  use  of  switches  for  this  service. 
It  is  desirable,  however,  to  use  a  type  of  switch 
which  can  be  opened  under  load.  It  is  often  desirable 
to  locate  section  breaks  at  passenger  stations  on  the 
"  far  side,"  in  order  to  enable  trains  to  reach  a 
station  in  spite  of  trouble  ahead. 

The  third  rail  may  be  sectionalized  for  another 
purpose  besides  confinement  of  accidents.  It  some- 
times occurs  that  the  current  normally  carried  by 
the  substation  circuit-breakers  is  of  such  unusual 
magnitude  that  the  circuit-breakers  are  materially 
damaged  whenever  they  operate.  It  is  therefore 


250  ELECTRIC   POWER  CONDUCTORS 

necessary  to  divide  the  third  rail  into  two  or  more 
sections,  each  of  which  is  directly  fed  from  the  sub- 
station by  feeders,  thereby  dividing  the  current 
between  two  or  more  circuit -breakers.  The  breaks 
at  substations  are  useful  in  effecting  the  same 
purpose. 

A  weak  point  in  the  ordinary  feeder  system  is 
found  in  the  cable  which  connects  the  bus  to  the 
third  rail.  Should  a  ground  occur  in  this  cable, 
it  will  not  suffice  to  open  the  breaker  between  it 
and  the  bus,  for  the  ground  will  be  fed  through  the 
third  rail  from  the  other  substations.  It  is  there- 


FIG.  56. — Third  Rails  Sectionalized  at  Passenger  Station. 

fore  desirable  to  have  a  switch  at  the  third  rail 
between  the  third  rail  and  its  feeder.  It  should  be 
remembered  that  a  ground  of  this  kind  will  neces- 
sitate the  interruption  of  current  from  all  sources 
and  may,  therefore,  seriously  delay  traffic. 

With  separately  fed  third  rails,  auxiliary  copper 
may  have  to  be  provided  for  each  rail,  whereas  with 
rails  connected  together,  auxiliary  copper  may  not 
be  required,  but  if  it  is,  it  will  serve  to  feed  all  the 
rails  and  may  be  connected  to  them  with  the  same 
system  of  switches  or  breaks  as  are  used  to  connect 
the  rails. 


TqiRD-RAIL  CIRCUITS  251 

A  much-discussed  subject  is  the  advisability  of 
using  short  isolated  sections  of  third  rail  at  gaps 
between  separately  fed  sections.  The  object  of  these 
is  to  prevent  a  car  or  train  from  spanning  across  a 
gap  between  a  live  and  a  grounded  rail.  With  the 
simple  multiple-unit  system — that  is,  where  only 
the  control  wiring  runs  from  car  to  car — an  isolated 
section  may  be  used  with  advantage.  It  must  be 
so  proportioned  as  to  render  it  impossible  for  one 
or  more  cars  to  span  both  gaps  which  isolate  the 
section,  and  the  section  on  each  track  must  be  fed 
through  a  separate  circuit-breaker.  When  a  bus 
line  connects  the  main  wiring  of  all  the  cars  a  short 
section  of  about  a  car  length  is  quite  useless.  In 
this  case  the  section  has  to  be  of  about  a  train 
length,  and  in  order  to  avoid  burning  out  the  train 
bus  line,  the  isolated  section  may  be  protected  by 
a  circuit-breaker  arranged  to  open  when  either  of 
the  main  third- rail  circuit-breakers  is  open.  A  train 
length  section  is  in  use  on  the  New  York  Central 
R.  R.,  where  it  has  been  of  considerable  service 
during  alterations  and  repairs  to  the  third  rails.  An 
alternative  scheme  which  has  been  found  satisfactory 
in  the  I.  R.  T.  subway,  New  York,  is  a  system  of  sig- 
nals at  the  gaps  arranged  to  show  danger  when  the 
rail  on  either  side  is  dead. 


CHAPTER  XI 

RAIL    BONDS 

CLASSIFICATION 


TABLE  I 

RAIL  BONDS 
CLASSIFIED  ACCORDING  TO  METHOD  OF  ADHESION 


I 
Chemical  Adhesion 


r 

Soldered  Bond 
(may  be  ap- 
plied to  Head, 
Web  or  Foot). 


Amalgamated 

or 

Bond. 


Plastic 


I 

Mechanical  Adhesion 
(Adhesion  is  obtained  by  expanding  ter- 
minal into  hole  in  the  rail.     Expansion 
effected  by  pressure  applied  in  follow- 
ing ways.) 


Brazed  Bond 
and  Welded 
Bond. 


Pressure  from 
inside.  Pin  Ex- 
panded Bond 
for  Web  or 
Foot. 

Pressure  from 
one  end.  Com- 
pressed Plead 
Bond. 


Pressure  from 
both  ends. 

Compressed 
Web  or  Foot 
Bond. 

252 


RAIL  BONDS 
TABLE  II 

RAIL  BONDS 
CLASSIFIED  ACCORDING  TO  TYPE  OF  CONDUCTOR 


253 


Solid 


Exposed 


Concealed 

I 


I 
Cable 


! 
Ribbon 


Solid 


Cable 


I 
Ribbon 


Classification.  Rail  bonds  differ  in  the  form  of  con- 
ductors, and  in  the  methods  of  securing  the  terminals 
of  the  conductor  to  the  rails.  Table  I  shows  the 
classification  according  to  the  method  of  securing 
adhesion  between  terminals  and  rail,  and  Table  II  the 
classification  according  to  type  of  conductor.  Each 
of  the  classes  mentioned  in  these  tables  is  commented 
on  below.  t 

Soldered  Bond  (Figs.  57,  58,  and  59).  Soldered 
bonds  are  very  easy  to  apply,  but  do  not  always  last 


/        FIG.  57. — Soldered  Bond  Head  Type. 

well.  Good  performance  for  several  months  should 
not  be  taken  as  a  guarantee  of  excellence,  because 
failures  only  begin  to  occur  after  several  months' 


254 


ELECTRIC   POWER  CONDUCTORS 


use.     Under  conditions  of  light  service  soldered  bonds 
are  quite  serviceable. 

When  soldered  bonds  become  loose  or  are  taken 


FIG.  58. — Soldered  Ribbon  Foot  Bond. 

off  for  rail  repairs   or  renewals,   they  can   be   used 
again. 

In  order  to  apply  a  soldered  bond,  the  rail  surface 
is  made  bright  with  an  emery  or  carborundum  wheel, 


FIG.  59. — Concealed  Soldered  Web  Bond. 

and  further  cleaned  with  hydrochloric  acid  before 
the  solder  is  put  on.  The  soldering  is  done  with  a 
blow  torch,  the  bond  being  held  in  place  with  clamps. 
Soldered  bonds  being  short  and  requiring  no  drill- 
ing, are  considerably  cheaper  than  most  other  kinds. 


RAIL  BONDS  255 

•  * 

Brazed  Bond.  Similar  to  soldered  bond  except  that 
brass  is  used  instead  of  solder. 

Welded  Bond  (Copper  Welding).  A  mould  is  set 
around  the  bond  terminal  and  back  along  the  rail 
a  little  distance,  and  then  some  copper  is  brought  to  a 
red  heat  in  a  crucible  placed  in  a  small  furnace  using 
hard  coal  or  coke  and  served  with  an  air  blast.  A 
portion  of  the  melted  copper  is  poured  through  a 
small  opening  in  the  mould  where  the  point  of  con- 
tact is  desired;  sufficient  is  poured  in  to  bring  the 
strands  of  the  bond  and  the  steel  to  the  welding  point, 
the  mould  being  provided  with  an  overflow  opening 
for  superfluous  copper.  When  it  has  solidified  the 
mould  is  taken  off  and  the  overflow  knocked  off  with 
a  hammer  to  be  used  again. 

The  heating  may  also  be  done  electrically  by  a 
process  similar  to  that  described  below  for  moulding 
rail  joints,  the  flat  copper  bond  head  being  welded  to 
the  rail. 

Plastic   Bonds.     The  conductivity  of  the  fish  plate 
is  made  use  of  by  interposing  between  it  and  the  rail 
a  copper  bond  brought  into  intimate  contact  with   . 
the  iron  with  the  aid  of  a  soft  mercury  amalgam. 

Another  type  has  a  copper  plate  which  makes 
electrical  contact  with  the  rail  by  means  of  a  plastic 
amalgam,  the  plate  itself  being  held  in  position  by 
the  reaction  of  a  spring  pressing  against  the  fish 
plate. 

The  latest  type  (Fig.  60)  consists  of  a  copper  plug 


256 


ELECTRIC   POWER  CONDUCTORS 


surrounded  with  amalgam,  placed  in  a  hole  drilled 
through  the  flange  of  a  girder  rail  and  into  the  fish 
plate. 

Bonds  with  Mechanical  Adhesion,  General.  These 
bonds  are  more  generally  used  than  any  other  type 
owing  to  their  greater  durability.  When  once  re- 
moved they  are  scrap  metal,  the  life  of  the  bonds 


FIG.  60. — Plastic  Bond  Plug  Type. 

being  therefore  limited  to  the  life  of  the  rails  on 
which  they  are  installed. 

There  are  a  great  many  different  types  on  the 
market  differing  principally  in  the  method  of  apply- 
ing the  terminal  to  the  rail.  There  is,  however,  little 
ground  for  discrimination  between  types. 

Drilling  of  the  rail  must  be  accomplished  without 


RAIL   BONDS 


257 


the  use  of  oil,  the  permissible  lubricants  being  soapy 
water  or  caustic  soda  solution. 

Pin-expanded  Bonds.  The  pin-expanded  terminal 
has  a  conical  hole  into  which  a  steel  pin  is  pressed 
by  screw  or  hydraulic  pressure.  This  presses  the 
copper  outward  into  firm  contact  with  the  rail  and 
leaves  a  head  on  the  outside  of  the  terminal  which, 
acting  like  a  rivet  head,  helps  to  hold  the  bond  firmly 
in  place. 

The  steel-core  type  resembles  the  ordinary  pin- 
expanded  type  in  many  respects,  but  the  steel  pin 


FIG.  61. — Pin  Expanded  Bond.     G.  E.  Co.  Type  with  Steel  Core. 

is  retained  in  the  terminal  after  it  is  installed.  The 
core  is  similar  to  a  double-headed  rivet  which,  when 
upset  by  longitudinal  compression,  expands  radially, 
forcing  the  walls  of  the  rail  hole  in  the  directions 
shown  by  the  arrows  in  Fig.  61. 

Compressed  Head  Bonds.  One  or  more  holes  are 
drilled  in  the  side  of  the  rail  head  and  the  bond  ter- 
minal pressed  firmly  into  the  hole  until  expanded 
sufficiently  to  hold  tight.  Reaming  the  sides  of  the 
hole  so  as  to  produce  cavities  to  catch  the  bond  head 


258 


ELECTRIC   POWER  CONDUCTORS 


does  not  add  much  to  the  security  of  this  type  of 
bond. 

If  constructed  so  that  rail  motion  will  not  tend  to 
rotate  the  bond  terminals  in  their  rail  holes,  this 
type  of  bond  is  very  satisfactory. 

Compressed  Web  or  Foot  Bond.  The  bond  terminal 
is  put  in  a  hole  drilled  through  the  rail  web  or  foot, 


FIG.  62. — Compressed  Bond.     Foot  Type. 

and  pressure  applied  at  both  ends  until  the  copper 
terminal  is  squeezed  into  the  shape  of  a  rivet,  its 
ends  being  spread  out  to  form  the  rivet  heads  (Figs. 
62,  63,  64,  and  65). 

Exposed  and  Concealed  Bonds.  Exposed  bonds  are 
desirable  on  account  of  the  facility  of  inspecting, 
where  there  is  little  danger  of  theft  or  external  injury. 

Concealed  bonds,  i.e.,  bonds  under  the  fish  plate, 
are  necessary  where  there  is  danger  of  theft  or  external 


RAIL  BONDS 


259 


injury.  Concealed  soldered  bonds  are  not  favored 
for  heavy  work  because  soldered  bonds  require  con- 
stant inspection  and  repairs. 

Head,  Web  and  Foot  Bonds.      Open  bonds   may  be 
applied  to  the  head,  web,  or  foot  of  the  rail. 


FIG.  63. — Compressed  Foot  Bond  and  Compressed  Concealed  Web  Bond. 

The  only  advantage  of  head  bonds  is  the  lower 
resistance  due  to  the  fact  that  most  of  the  current 
in  a  rail  is  carried  in  the  head.  This  type  of  bond 
is  practical  for  third  rails  only,  on  account  of  th3 
wear  on  the  heads  of  track  rails. 

Web  bonds  are  commonly  used  because  concealed 
bonds  are  necessarily  of  that  type  and  expanded 


260  ELECTRIC  POWER  CONDUCTORS 

terminal  bonds  are  most  conveniently  applied  to  the 
web. 

Foot  bonds  are  little  used  except  for  third-rail  work. 


FIG.  64. — Protected  Ribbon  Bond  with  Compression  Terminals. 

Soldered  bonds  are  most  easily  applied  to  the  upper 
surfaces  of  the  foot,  while  compressed  terminal  bonds 
are  more  generally  applied  underneath. 


FIG.  65.— Solid  Wire  Bond. 

Solid,  Cable,  and  Ribbon  Bonds.  Bonds  of  all 
classes  are  made  either  of  solid  copper,  stranded 
cable,  or  multiple  ribbons  of  copper. 

Solid    bonds,    unless    of    great    length    and    small 


RAIL  BONDS  261 

X    9 

cross-section,  are  too  stiff  for  traction  work,  but 
are  largely  used  for  signal  and  telegraph  circuits. 

Exposed  bonds  are  usually  of  wire  cable,  as  on 
account  of  its  flexibility  in  all  directions  this  mate- 
rial is  well  adapted  to  withstand  vibration. 

Ribbon  bonds  are  usually  used  under  fish  plates 
on  account  of  their  compactness  and  the  ease  with 
which  they  lend  themselves  to  tucking  about  the 
fish-plate  bolts. 

Efficiency  of  Bonding.  The  efficiency  of  a  rail 
bond  is  the  ratio  of  the  conductivity  of  the  bonded 
joint  to  the  conductivity  of  an  equivalent  length 
of  continuous  rail.  If  a  rail  of  length  L  has  a  sec- 
tional area  equivalent  to  A  c.m.  of  copper,  and  a 
bonded  joint  of  length  /  has  a  section  equivalent  to 
a  c.m.,  the  efficiency  of  the  bonded  joint  neglecting 

contact  resistance  is  —  =  /. 
J\. 

The  efficiency  of  the  bonding  of  a  line  of  rail  is  the 
ratio  of  the  conductivity  of  the  bonded  line  to  the 
conductivity  of  the  line,  supposing  the  rail  to  be 
continuous. 

The  relation  between  the  efficiency  of  the  bond- 
ing of  a  line  and  the  efficiency  of  a  bonded  joint  is 
given  by  the  equation, 

Efficiency  of  the  bonding  of  line  = . 

L  + -(i-/) 

Fig.  66  shows  this  equation  plotted  as  a  curve  for 


262 


ELECTRIC  POWER  CONDUCTORS 


L  =  6o  and  £  =  3.  It  will  be  noted  that  the  bond 
efficiency  may  be  very  low  without  materially  reduc- 
ing the  efficiency  of  the  bonded  line.  It  therefore 
appears  that  the  size  of  bond  to  be  adopted  depends 


80        30        40        60        CO        70        80        90      10* 

Per  Cent 
BOND  OF  EFFICIENCY  OF  JOINT. 

RELATION  BETWEEN  BOND  EFFICIENCY  OF  JOINT  AND  OF  LINE. 

FIG.  66. 

more    upon    the    carrying    capacity    than    upon    the 
conductivity. 

Carrying  Capacity  of  Bonds.  The  carrying  ca- 
pacity of  a  bond  cannot  be  calculated  by  the  ordi- 
nary rules  for  wires  or  ribbons,  on  account  of  the 
great  cooling  effect  of  the  rails.  A  soldered  bond 
will  become  loose  on  account  of  the  fusion  of  the 
solder  without  the  copper  being  in  any  way  injured. 


,   RAIL  BONDS 


263 


Thus  a  No.  oooo  soldered  bond  will  melt  off  in  five 
or  ten  minutes  at   10,000  amperes. 

It    should    be    noted    that    short    bonds    have    far 
greater  carrying  capacity  than  long  bonds  on  account 


V2M.C.M    OOB.&.S  OCOOB.&S.  V2M.C.M. 


20 


10 


/ 

i 

/ 

/ 

7 

/ 

/ 

/ 

/ 

800 

/ 

/ 

/ 

1 

7 

/ 

/ 

700 

/ 

/ 

/ 

y 

1 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

I 

500 

/ 

/ 

i 

1 

/ 

7 

/ 

/ 

/ 

1 

/ 

/         y 

/ 

1 

5 

/ 

/ 

y 

i 

/ 

i 

/ 

/ 

/ 

/ 

j 

/  > 

/ 

y 

/ 

1 

d 

i 

, 

V 

/ 

/ 

H 
200 

/ 

/ 

/ 

/ 

2 

/ 

/ 

/ 

100 

4  5         6        7       8     9    10 

Thousands  of  Amperes 


FIG.  67. — 9-in.  Bond  with  Mechanical  Adhesion. 

of  the  proportionately  greater  cooling  effect  of  the 
rails. 

There  is,  at  the  present  time,  little  reliable  data 
on  the  carrying  capacity  of  the  various  types  of  bonds. 

The  diagram  (Fig.  67)  refers  to  a  Q-in.  exposed 
bond  with  mechanical  adhesion  or  welded.  The 
heavy  lines  should  be  used  in  connection  with  the 


264 


ELECTRIC  POWER  CONDUCTORS 


right-hand    temperature    scale,    and    the    light    lines 
with  the  left-hand  temperature  scale. 

Importance  of  Cleanliness  in  Bonding.  In  order 
to  secure  good  bonding  it  is  essential  to  guard  against 
dirty  bonds,  and  bond  holes,  rough  and  irregular 
bond  holes  insufficient  pressure  on  compressed  ter- 
minals, unclean  rails,  and  insufficient  heat  on  sol- 
dered bonds.  The  average  track  construction  gang, 
if  entrusted  with  bonding,  even  under  the  eyes  of 
a  vigilant  inspector,  usually  makes  joints  which, 
while  mechanically  good,  are  electrically  imperfect. 
For  this  reason  many  companies  now  have  special 
bonding  forces  under  a  foreman  with  sufficient 
electrical  training  to  understand  the  importance  of 
good  electrical  contact. 


TABLE  III 

CIRCULAR    MILS    OF    COPPER    EQUIVALENT    TO    VARIOUS 
WEIGHTS  OF  RAIL 


Weight 

Ratio  of  Resistance  of  Steel  to  Resistance  of  Copper! 

of 

Rails, 

» 

Lbs. 

per 
Yard. 

6. 

7- 

8. 

9- 

10. 

ii. 

12. 

5° 

1,061,030 

9°9,455 

795,773 

707,354 

636,618 

578,743 

53°,5I5 

60 

1,273,236 

1,091,346 

954,928 

848,825 

763,942 

694,491 

636,618 

70 

1,485,442 

1,273,237 

1,114,083 

990,296 

891,266 

810,239 

742,721 

75 

1,591.545 

1,364,183 

1,193,660 

1,061,031 

954,927 

868,115 

795,773 

80 

1,697,648 

1,455,127 

1,273,238 

1,131,766 

1,018,589 

925,989 

848,825 

90 

1,909,854 

1,637,018 

i,432,393 

1,273,237 

1,145,913 

1,041,735 

954,928 

100 

2,122,060 

1,818,910 

1,591,546 

1,414,708 

1,273,236 

1,157,486  1,061,030 

RAIL  BONDS  265 

$ 

Single  and  Double  Bonding.  Single  bonding 
has  the  advantage  of  being  more  likely  to  be  in 
good  repair,  as  a  defective  bond  soon  reveals  itself. 
Double  bonding  affords  a  factor  of  safety  very  im- 
portant on  busy  roads. 

Welded  Rail  Joints.  Both  bonding  and  the  mechan- 
ical connection  of  rails  are  replaced  by  various 
types  of  welded  joints,  although  some  companies 
use  the  welded  joint  for  its  mechanical  features 
only,  preferring  to  use  copper  bonds  to  maintain 
electrical  continuity. 

CAST  WELDING 

A  mould  is  placed  around  the  rail  joint  and  molten 
iron  poured  into  it. 

There  are  various  ways  of  effecting  this,  differing 
in  the  type  of  mould  and  method  of  applying  the 
iron,  but  in  all  of  them  thorough  cleansing  of  the 
rails  at  the  joints  and  protection  of  the  rail  top 
from  molten  metal  are  of  prime  importance. 

It  is  claimed  by  some  that  cast  welding  changes 
the  character  of  the  steel  at  the  joints  so  that  the 
joints  do  not  wear  the  same  as  the  rest  of  the  track, 
and  will  in  time  hammer  down.  This  is  apparently 
due  to  defects  in  workmanship,  as  this  trouble  is  not 
experienced  by  all  users  of  cast  welded  joints. 

It  is  important  to  use  plenty  of  metal  in  order 
that  it  may  not  be  too  rapidly  chilled. 


266  ELECTRIC  POWER   CONDUCTORS 


THERMIT  WELDING 

A  mould  is  placed  around  the  rail  joint,  and  molten 
iron  poured  into  it.  The  process  differs  from  the 
ordinary  cast  weld  in  the  method  of  preparing  the 
molten  iron. 

Preparing  the  Rails.  The  rails  having  been 
aligned  properly,  the  ends  are  thoroughly  cleaned 
with  a  sand  blast  or  wire  brush  a  few  inches  each 
side  of  the  joint.  The  rails  are  then  heated  by  a 
gasoline  or  oil  blow  torch,  to  expel  all  moisture. 
Some  advise  heating  to  a  dull  red  heat. 

The  Moulds.  The  moulds  consist  of  iron  frames 
lined  with  a  mixture  of  sand  and  10%  cheap  rye 
flour.  This  mixture'  is  slightly  moistened,  so  as 
to  retain  its  form  when  pressed  in  the  hands,  and 
in  this  condition  placed  in  the  iron  frames  and 
baked  at  about  the  same  temperature  as  bread. 
By  adding  a  teaspoonful  of  turpentine  to  each  pair 
of  moulds,  the  material  is  hardened.  This,  however, 
is  unnecessary  except  for  special  work. 

The  mould  frames  are  securely  clamped  to  the 
rails,  one  on  each  side,  the  interstices  between 
moulds  and  rails  luted  with  clay  about  the  consis- 
tency of  putty,  and  common  earth  heaped  around 
the  frames. 

The  rail  head  is  then  painted  with  a  watery  paste 
of  common  red  clay,  which  the  heated  rail  imrne- 


RAIL  BONDS  267 

-  * 

diately  dries  to  a  thin  coating.  This  is  to  prevent 
the  molten  steel  uniting  with  or  burning  the  rail 
head. 

The  moulds  and  rails  are  then  given  a  final  warm- 
ing with  the  torch. 

The  Crucible  and  its  Use.  The  crucible  on  its  tripod 
is  placed  with  its  pouring  hole  directly  over  and 
about  two  inches  above  the  gate  in  the  mould.  After 
placing  the  topping  pin,  iron  disk,  asbestos  disk, 
and  refractory  sand  in  the  bottom  of  the  crucible  to 
act  as  a  plug  for  the  opening,  the  thermit  compound 
is  poured  in  and  in  the  center  of  the  top  is  placed 
about  one-third  of  a  teaspoonful  of  ignition  powder, 
which  is  set  off  with  a  match. 

The  compound  is  composed  of  a  mixture  of  iron 
oxide  and  aluminum,  both  in  granular  or  flake  form. 
The  ignition  powder  is  composed  of  barium  peroxide 
and  aluminum  in  fine  powder.  When  the  match  is 
applied  to  the  ignition  powder,  the  aluminum  ignites, 
drawing  the  necessary  oxygen  from  the  barium  per- 
oxide. The  heat  thus  developed  ignites  the  aluminum 
of  the  thermit  compound,  which  draws  the  oxygen 
from  the  iron  oxide  and  liberates  the  iron.  The 
latter  settles  immediately  to  the  bottom  of  the  cru- 
cible. While  this  is  going  on,  the  contents  of  the 
crucible  form  a  glowing,  seething  mass,  and  in  about 
thirty  seconds  the  action  is  completed. 

The  crucible  is  tapped  by  striking  the  tapping  pin 
with  a  special  iron  spade,  and  the  incandescent  steel 


268  ELECTRIC  POWER  CONDUCTORS 

runs  smoothly  into  the  mould,  the  slag  following. 
In  five  minutes  the  mould  can  be  removed  to  permit 
the  passage  of  cars. 

The  mould  must  be  of  generous  proportions,  other- 
wire  the  rail  will  chill  the  iron  and  the  latter  will 
not  adhere. 

It  is  found  that  if  thermit  welding  is  performed 
when  the  temperature  is  rising,  the  expansion  of  the 
rails  is  apt  to  cause  a  hump  at  the  joints. 

For  this  reason  it  is  better  to  work  on  cool  days  or 
when  the  temperature  is  falling. 

ELECTRIC  WELDING 

An  iron  bar  is  fitted  against  the  web  of  the  rail 
and  welded  thereto  by  heating  both  the  bar  and  the 
rail  to  a  white  heat  by  means  of  an  electric  current. 

Preparing  the  Rails.  The  rails  having  been  aligned 
properly,  the  ends  are  thoroughly  cleaned  with  a 
sand  blast  or  wire  brush  a  few  inches  along  both 
sides  of  the  web.  The  iron  bars  are  applied  one  on 
each  side  of  the  web  and  clamped  to  one  rail. 

Source  and  Application  of  Current.  A  small  motor 
generator  set  on  a  wagon  is  operated  by  power  taken 
from  the  trolley,  and  supplies  alternating  current  to 
a  step-down  transformer.  The  secondary  of  this 
transformer  supplies  current  at  very  low  voltage  but 
enormous  amperage  which,  when  applied  to  the 
clamps  which  hold  the  bars  to  the  rails,  brings  both 
bars  and  rails  to  a  white  heat  and  welds  them  into  one. 


RAIL  BONDS 


•   * 


While  still  hot,  the  bars  are  clamped  to  the  other 
rail  and  the  current  applied  until  the  welding  is 
effected.  As  the  bars  cool,  they  contract  and  draw 
the  rails  firmly  together. 

Iri  order  to  obtain  good  results  the  rails^must  be 
well  abutted  before  welding. 

TABLE  IV 

BONDING  AREAS 
INTERNAL  CONTACT  AREA  OF  HOLE  IN  RAIL 


Diameter, 
Inches. 

Length 
i  Inch 

Length 
A  Inch. 

Length 
|  Inch. 

Length 
2\  Inch. 

Length 
2i  Inch. 

Sq.In. 

Sq.In. 

Sq.In. 

Sq.In. 

Sq.In. 

1 

1.964 

1.105 

1.232 

4-419 

4.918 

f 

2-356 

i-324 

1.471 

5-298 

5.890 

I 

2-749 

i-545 

1.721 

6.185 

6.871 

I 

3-*42 

1.767 

1.962 

7.068 

7-854 

l£ 

3-338 

1-875 

2-085 

7-509 

8-345 

l| 

3-927 

2.206 

2.452 

7-825 

9.818 

I* 

4.712 

2.648 

2.941 

10.602 

i  i  .  780 

If 

5-498 

3.088 

3-436 

12.371 

13-745 

2 

6.283 

3-528 

3-925 

14-137 

15.708 

ai 

7.069 

3-974 

4.418 

15-905 

17.673 

a* 

7-854 

4.418 

4-913 

17.672 

19-635 

CROSS-SECTION  OF  BONDS  IN  C.M.  AND  SQ.IN. 


C.M. 

Sq.In. 

C.M. 

Sq.In.       |          C.M. 

Sq.In. 

1,000,000 

0.785 

400,000 

0.314 

200,000 

°-I57 

900,000 

0.707 

350,000 

0.275 

000 

o.  132 

800,000 

0.628 

300,000 

0.236 

00 

0.104 

750,000 

0.489 

250,000 

0.196 

125,000 

0.098 

600,000 

0.472 

225,000 

0.177 

o 

0.083 

500,000 

0-392 

0000  * 

0.166 

100,000 

0.079 

450,000 

o-354 

*B.&S. 


CHAPTER  XII 
INDUCTANCE,   REACTANCE,  AND  CAPACITY 

i.     TABLES    OF    INDUCTANCE    AND    REACTANCE 
OF  PARALLEL  WIRES  * 

Inductance  of  Single  Phase  Lines.  To  find  the  in- 
ductance in  millihenrys  per  mile  of  each  of  two 
parallel  non-magnetic  wires,  find  A  corresponding  to 
the  distance  apart  of  the  wires,  and  B  corresponding 
to  the  size  of  wire,  and  add  together  A  and  B.  The 
sum  will  be  the  required  inductance. 

Thus  the  inductance  of  a  1,000,000  circular  mil 
cable,  distant  50  feet  from  a  similar  cable,  will  be 

2.724  — .363  =2.36  millihenrys  per  mile. 

The  inductance  of  a  No.  36  wire,  distant  10  inches 
from  a  similar  wire,  will  be 

1.407  +  1.338  =  2.745. 

Reactance.  Express  L  in  millihenrys.  Then  if 
/  =  cycles  per  second, 

Reactance  =  2  X  io~37r/L. 

*  See  Appendix  VII. 

270 


INDUCTANCE,   REACTANCE  AND  CAPACITY     271 

To  find  the  reactance  in  ohms  per  mile  of  each  of  two 
parallel  wires,  find  a  corresponding  to  the  distance 
apart  of  the  wires,  and  b  corresponding  to  the  size  of 
wire,  and  add  together  a  and  b.  The  sum  will  be  the 
reactance  at  100  cycles.  At  other  frequencies  the  re- 
actance will  be  in  proportion  to  the  frequency. 


TABLE  I 

SINGLE  PHASE 
VALUES  OF  A 


d,  Distance 
between 
Centers  of 
Wires,  Ins. 

A. 

d.  Distance 
between 
Centers  of 
Wires,  Ins. 

A. 

d.  Distance 
between 
Centers  of 
Wires,  Ins. 

A. 

I 

0.6654 

21 

-6^5 

41 

.861 

2 

0.8886 

22 

.660 

42 

.868 

3 

1.019 

23 

-675 

43 

.876 

4 

1.  112 

24 

.688 

44 

-883 

5 

.183 

25 

.701 

45 

.891 

6 

.242 

26 

.714 

46 

.898 

7 

.292 

27 

.726 

47 

-905 

8 

-335 

28 

-738 

48 

.911 

9 

-373 

29 

-749 

49 

.918 

10 

.407 

30 

.760 

5° 

-925 

it 

-437 

31 

.771 

Si 

-931 

12 

-465 

3  2 

.781 

52 

-937 

13 

.491 

33 

.791 

53 

-943 

14 

-5i5 

34 

.800 

54 

-949 

iq 

-537 

35 

.810 

55 

-955 

16 

-558 

36 

.819 

56 

.961 

17 

-577 

37 

.828 

57 

.967 

18 

-596 

38 

.836 

58 

.972 

19 

.613 

39 

-845 

59 

.978 

20 

.630 

40 

1-853 

60 

-983 

272 


ELECTRIC  POWER  CONDUCTORS 


TABLE  II 

SINGLE  PHASE 
VALUES  or  A 


d.  Feet. 

A. 

d.  Feet. 

A. 

d,  Feet. 

A. 

I 

1.465 

15 

2.336 

29 

2-549 

2 

1.688 

16 

2-357 

3° 

2.560 

3 

1.819 

i? 

2.368 

35 

2.609 

4 

1.911 

18 

2-395 

40 

2.652 

5 

1-983 

19 

2-413 

45 

2.690 

6 

2.042 

20 

2.428 

5° 

2.724 

7 

2.091 

21 

2-445 

60 

2.783 

8 

2-134 

22 

2.460 

70 

2.832 

9 

2.172 

23 

2.474 

80 

2-875 

10 

2.206 

24 

2.488 

90 

2.913 

ii 

2.237 

25 

2.501 

100 

2.947 

12 

2.265 

26 

2-513 

500 

3-465 

13 

2.290 

27 

2.525 

IOOO 

3.688 

14 

2.314 

28 

2-537 

TABLE  III 

SINGLE  PHASE 
VALUES  or  B 


Size  of  Wire 
No.  B.&S. 

B. 

Size  of  Wire, 
No.  B.  &  S 

B. 

Size  of  Wire, 
No.  B.  &  S. 

B. 

oooo 

—  O.II2 

II 

0.411 

24 

0.896 

ooo 

-0.075 

12 

0.448 

25 

0-933 

00 

-0.037 

13 

0.485 

26 

0.970 

0 

0 

14 

0.522 

27 

.008 

I 

0.037 

15 

0.560 

28 

.044 

2 

0.075 

16 

o-597 

29 

.082 

3 

O.II2 

i7 

0.634 

3° 

.120 

4 

0.149 

18 

0.672 

3i 

-157 

5 

0.187 

19 

0.709 

32 

.194 

6 

0.224 

20 

0.746 

33 

.232 

7 

o.  261 

21 

0.784 

34 

.269 

8 

0.298 

22 

0.822 

35 

.306 

9 

°-336 

23 

0.859 

36 

-344 

TO 

°-373 

INDUCTANCE,^  REACTANCE  AND  CAPACITY    273 


TABLE  IV 

SINGLE  PHASE 

VALUES  OF  a 
=  0.46565  log  d+  0.41811) 


Distance  between 
Centers  of  Wires, 
Inches  =  d. 

a. 

Distance  between 
Centers  of  Wires, 
Inches  =  d. 

a. 

I 

0.4181 

21 

-0338 

2 

0.5626 

22 

.0432 

3 

0.6413 

23 

.0522 

4 

0.7071 

24 

.0608 

5 

0.7436 

25 

.0691 

6 

0.7805 

26 

.0770 

7 

0.8116 

27 

.0846 

8 

0.8386 

28 

.0920 

9 

0.8625 

29 

.099! 

10 

0.8838 

3° 

.1059 

ii 

0.9030 

36 

.1428 

12 

0.9206 

42 

.1740 

13 

0.9368 

48 

.2OIO 

14 

0.9518 

54 

.2248 

15 

0.9658 

60 

.2461 

16 

0.9788 

66 

.2654 

17 

0.9911 

72 

.2830 

18 

1.0026 

78 

.2992 

19 

1.0136 

84 

•3*42 

20 

1.0239 

90 

.3281 

96 

.3412 

Thus  the  reactance  at  25  cycles  of  a  mile  of  No. 
oooo  B.  and  S.  36  in.  between  wires,  is   as  follows: 

a=      1.1428 
b=—    .0703 


dividing  by 


1.0725 
100 


.2681  ohm. 


274 


ELECTRIC  POWER  CONDUCTORS 


TABLE  V 

SINGLE  PHASE 
VALUES  or  b 
(6  =  0.023443;?) 


Size  of  "Wire. 

b. 

Size  of  Wire. 

b. 

1,000,000  C.M. 

—  o.  2272 

7 

o.  1641 

750,000  C.M. 

—  0.1982 

8 

0.1876 

500,000  C.M. 

-0.1572 

9 

0.2IIO 

250,000  C.M. 

—  0.0872 

10 

0.2344 

oooo  B.  &  S. 

—  0.0703 

ii 

0.2579 

000 

—  0.0469 

12 

0.2813 

oo 

-0-0235 

J3 

0.3048 

o 

o 

14 

0.3282 

I 

0.0235 

15 

0-35*7 

2 

0.0469 

16 

o-375i 

3 

0.0703 

17 

0.3986 

4 

0.0938 

18 

0.4220 

5 

0.1172 

i9 

0-4454 

6 

0.1407 

20 

0.4689 

n  is  the  number  of  the  wire  on  the  B.  &  S.  g-uge. 

Impedance. 

v7Resistance2  +  reactance2  =  impedance. 

In  a  three  phase  line  with  wires  symmetrically 
arranged  the  reactive  drop  in  the  loop  formed  by 
any  two  wires  is  V$  X  reactance  of  each  wire  X  cur- 
rent in  the  wire. 

Inductance  for  Parallel  Iron  Wires  (approximate). 
d  =  distance  apart,  center  to  center ,  of  wires. 
r  =  radius  of  wires. 

L  =  inductance  of  each  wire  in  millihenry s. 
Formulae, 

^  =    75  +  (2  l°g:~~)    I0~6>  Per  centimeter. 


INDUCTANCE,   REACTANCE  AND  CAPACITY     275 


L  per  centimeter  =  .000,075  +  .000,004,6    log-. 

d 

L  per  inch  =.000,191  +  .000,011,68  log  -. 


L  per  foot 

L  per  1000  feet   =2.286       +.14 


=.002,  286  +  .000,  14        log-. 

log-. 
d 


=  12.070       +.741  log-. 


L  per  mile 

(Permeability  assumed  to  be  150.) 
TABLE  VI 

APPROXIMATE  OHMIC  RESISTANCE  AND  IMPEDANCE  OF 
THREE  CONDUCTOR  CABLES 


IMPEDANCE  OHMS  PER  MILE. 

Size. 

ance, 
Ohms 

Working  Voltage. 

per  Mile. 

3000 

5000 

7000 

JOOOO 

15000 

20000 

2 

0.850 

0.858 

0.859 

0.863 

0.867 

0.872 

0.884 

I 

0.674 

0.692 

0.696 

0.700 

0*706 

0.712 

0.724 

o 

0-535 

o-545 

0-547 

o-552 

0.558 

°-565 

0.580 

00 

0.424 

0.436 

o-439 

0.444 

0.452 

0.460 

0.478 

000 

o-336 

0-352 

0-352 

o-357 

0.365 

o-374 

0.396 

0000 

0.267 

0.280 

0.283 

0.288 

0.296 

0.306 

0-332 

250,000 

0.227 

0.245 

0.245 

0.252 

0.261 

0.272 

0.299 

300,000 

0.188 

O.2IO 

0.210 

0.217 

0.227 

0.241 

O.27O 

350,000 

0.161 

0.187 

0.187 

0.194 

o.  204 

0.217 

0.250 

400,000 

0.141 

0.166 

0.166 

0.174 

0.185 

0.199 

0-234 

450.000 

0.127 

0.148 

0.148 

0.156 

0.167 

0.182 

O.22I 

500,000 

0-113 

o  137. 

0.137 

0.144 

0.156 

0.172 

O.2I2 

Based  on  pure  copper  at  75°  F.  with  an  allowance  of  3%  for  spiral  path  of  con- 
ductors, 60  cycles  per  second,  and  standard  thickness  of  varnished  cambric  insu- 
lation. * 

Values  are  practically  the  same  for  other  types  of  insulation. 

NOTE. — These  figures  are  approximately  correct  for  98%  conductivity  copper  at 
65°  F.— G.  E.  Co.  Bulletin. 


276 


ELECTRIC  POWER  CONDUCTORS 


Overcoming  Effects  of  Mutual  Induction.  Neighbor- 
ing circuits  having  currents  of  the  same  frequency 
affect  each  other  so  that  the  inductive  drop  in  one 
circuit  is  increased,  and  in  the  other  decreased.  If 
the  currents  differ  in  frequency,  the  potential  will 
rise  in  one  circuit  when  the  waves  come  in  step, 
and  will  fall  in  the  other  circuit. 


1  1 

O   0 

44    44 

00     0   O 

33    33 

O   O     O   0 

22     22 

00     00 

1  1 

0  O 

2   2 

0   0 

33     11 

00      00 

22    44 

O  O     O  O 

11     33 

00      00 

4  4 

O  0 

. 

. 

FIG.  68. 

The  simplest  cure  for  this  evil  is  to  put  the"  wires 
of  a  circuit  close  together  compared  with  their 
distance  from  the  other  circuit.  Another  way  is 
to  transpose  the  wires  so  that  the  induction  along 
one-half  the  line  will  neutralize  the  induction  in  the 
other  half.  This  is  illustrated  in  Fig.  68,  in  which 
each  diagram  shows  how  the  wires  should  be  arranged 
for  one-quarter  of  the  entire  length. 


INDUCTANCE,  REACTANCE  AND  CAPACITY     277 


2.  CAPACITY 

General.  The  capacity  of  a  transmission  line  is 
distributed  over  the  whole  length  of  the  conductor, 
so  that  the  circuit  can  be  considered  as  shunted  by 
an  infinite  number  of  infinitely  small  condensers 
scattered  along  its  entire  length.  Where  the  capac- 
ity of  the  line  is  small,  however,  it  may,  with  suffi- 
cient approximation,  be  represented  by  one  con- 
denser of  the  same  capacity  as  the  line,  shunted 
across  the  line,  either  at  the  generator  end,  the 
receiver  end,  or  at  the  middle. 

The  best  approximation  is  to  consider  the  line 
as  shunted  at  the  generator  and  at  the  receiver  end, 
by  two  condensers  of  one-sixth  the  line  capacity  each, 
and  in  the  middle  by  a  condenser  of  two-thirds  the 
line  capacity.  This  approximation,  based  on  Simp- 
son's rule,  assumes  the  variation  of  the  electric 
quantities  in  the  line  as  parabolic. 

(Abstracted  from  "  Alternating  Current  Phenom- 
ena," C.  P.  Steinmetz.) 

Injurious  Effects  of  Capacity.  The  principal  objection 
to  high  capacity  in  a  line  is  the  large  charging  current 
which  necessitates  a  greater  generating  and  transform- 
ing equipment.  The  current,  being  wattless,  does  not 
give  rise  to  much  energy  loss. 

In  case  the  line  is  supplying  a  low  power  factor  load, 
a  high  capacity  in  the  line  may  be  a  distinct  advan- 


278  ELECTRIC  POWER  CONDUCTORS 

tage,  as  it  improves  the  power  factor  at  the  generat- 
ing station  by  neutralizing  the  lagging  current  taken 
by  the  load. 

Two  Parallel  Wires  (Bare).  The  capacity  given  by 
the  following  formulae  are  for  the  pair  of  wires,  such 
a  pair  forming  with  the  air  between  them,  the  equiva- 
lent of  a  condenser. 

,_..       f  .,  .038,83 

Microfarads  per  mile,  , 


Microfarads  per  1000  ft., 


'-  — 
log  — 


.  .000,02415 

Microfarads  per  meter,     -,  -  r)> 

log  — 
where  r 

r  =  radius  of  wire; 

D=  distance  apart,  center  to  center. 
The  logarithms  are  to  the  base  10. 

In  the  above  formulse  it  is  assumed  that  the  dis- 
turbing effect  of  the  earth  and  other  neighboring  con- 
ductors, is  negligible. 

Charging  Current. 

E=  potential  difference  between  wires,  volts; 
K  =  capacity  in  microfarads  of  the  condenser 

formed  by  any  two  line  wires; 
/  =  frequency  in  cycles  per  second; 
I  =  charging  current,  amperes  per  wire; 


INDUCTANCE,  REACTANCE  AND  CAPACITY    279 
* 

For  a  single  phase  line, 


For  a  three  phase  line, 
/  = 


V3  X  io6 


Single  Overhead  Wire  with  Earth  Return. 

h  =  height  of  wire  above  ground, 
r=  radius  of  wire. 

(These  to  be  given  in  the  same  units.) 

The  capacity  of  such  a  wire  is  equal  to  that  of  a 
pair  situated  a  distance  2h  apart.  In  other  words,  the 
capacity  which  such  a  wire  forms  with  the  earth  is 
equal  to  that  which  it  forms  with  its  reflected  image 
in  the  earth,  assuming  the  earth  to  be  a  perfect  con- 
ductor. 

Microfarads  per  mile, 


Microfarads  per  1000  ft.,     • — ; 

,      2h 
log  — 
r 

.000,0241  c 
Microfarads  per  meter,         r—^ 

log^ 


280  ELECTRIC  POWER  CONDUCTORS 

Single-Phase  Two  Conductor  Cable. 

Let  a  =  capacity    between    one    conductor    and    the 

other  in  parallel  with  the  sheathing; 
b  =  —  (a  —  |  capacity  between  the  two  conductors 
in  parallel  and  the  sheathing) . 

These  two  are  readily  measurable  quantities.  Then 
the  capacity  between  the  two  conductors  equals 
|.<a,-6), 

Three-Phase  Cable  with  Neutral  Grounded. 

Let  a  =  capacity  between  one   wire   and   the   other 

two  in  parallel  with  the  sheathing, 
b  =  —  (a  —  |    capacity    between    two    wires    in 
multiple  and  one  wire  and  sheathing  in 
multiple) . 

These  two  are  readily  measurable  quantities.     Then 

Capacity  between  one  wire  and  other  two  in 

parallel  with  the  sheathing  =a; 

Capacity  between  two  wires  in  multiple  and 

one  wire  and  sheathing  in  multiple  =  2  (a  +  b) ; 

Capacity  between  three  wires  in  multiple 

and  the  sheathing  =  3  (a  +  2-b) 

Capacity  between  two  wires  =  J  (a  —  b) ; 

Capacity    between   one   wire   and   two   in 

multiple  =  f  (a  —  b) 

(Alex.    Russel,    Journal   Inst.  Elect.  Eng.,  London, 
1901.) 


APPENDIX  I 

BASIS  OF   AMERICAN    OR    BROWN  AND 
SHARPS  GAUGE 

THE  American  or  Brown  and  Sharpe  gauge  is  based 
upon  a  geometrical  progression  beginning  with  a 
wire  of  five  mils  diameter,  called  No.  36,  and  ending 
with  a  wire  of  460  mils  diameter,  called  No.  oooo. 
These  numbers  and  sizes  were  selected  in  order  to 
make  the  gauge  conform  approximately  with  exist- 
ing systems. 

The  ratio  of  this  geometrical  progression  is 


Rm»J?Z.        «V92=  I.I22932 

and  its  common  logarithm  is 

•°5°>353>53- 

The  diameter  of  a  No.  n  wire  is  that  of  a  No.  o 
wire  divided  by  Rn,  and  as  the  diameter  of  a  No.  o 

281 


282  ELECTRIC,  POWER  CONDUCTORS 

wire  is  that  of  a  No.  oooo,  divided  by  -R3,  the  diameter 
of  a  No.  n  wire  in  mils  is  equal  to 

460 
•^3,  exactly, 

32,486 
or,  — ,  approximately. 

I.J229n 

The  area  in  circular  mils  being  equal  to  the  square 
of   the  diameter,  •  is   equal   to 

211,600 


R 


2n+G 


-,  exactly, 


or  ,  approximately. 

1.2605" 

The  number  on  the  B.  and  S.  gauge  of  a  conductor 
of  A  circular  mils  area  is  given  by  the  following 
equation,  which  is  derived  from  the  above  equation 
for  area, 


/  2ii,6oo\ 

or  n  =  (9.92978  log — )— 3- 

\  A      / 

, 
Numbers  of  conductors  larger  than  No.  o  are  given 

as  negative  quantities.     Thus 

B.  and  S.  No.  n 

O  O 

00  —  I 

OOO  —2 

oooo  —  3 

etc. 


APPENDIX  I  283 

•  * 
The  ratio  R  is  approximately  equal  to  the  sixth 

root  of  2,  which  is  1.12246.  This  fact  makes  it 
possible  to  have  a  group  of  wires  having  approxi- 
mately the  same  area  as  any  single  wire,  all  being 
regular  sizes  on  the  B.  and  S.  gauge.  This  approxi- 
mation gives  rise  to  the  following  formulae: 

Diameter,  mils         ='    n    ; 

26" 

105,500 
•     Area,  circ.  mils.        = — =~ — 

23" 


Ohms,  per  1000  ft.  =— ; 
10 

-220 
Pounds  per  1000  ft.  =^-. 

23" 


APPENDIX  II 

BASIS    OF    SKIN    EFFECT    AND    CARRYING- 
CAPACITY  FORMULAE 

SKIN  EFFECT 

USING  the  same  symbols   as  on   p.   40,  the  exact 
expression  for  R  is  as  follows: 

7?__i   ker-  />-bei'.  p  —  bei.  p-ber.'  p 
' 


where  £  =  0.875  Z,  arid  0.875  *s  the  square  root  of  STT 
times  the  number  of  centimeters  in  one  foot. 

Bessel's  functions  may  be  avoided  by  substituting 
a  series,  but  for  all  practical  purposes  the  approxima- 
tion given  is  sufficient. 

CARRYING  CAPACITY 

A  conductor  heated  by  a  current  assumes  a  steady 
temperature  when  the  power  generated  in  it  equals 
the  power  dissipated  from  it.  The  rate  of  generation 
of  heat  is  given  by  the  well  known  equation 

Pk 

Watts  =  —  , 
a 

284 


APPENDIX  II  285 

where  /  =  amperes  ; 

k  =  specific  resistance  of  conductor  in  ohms  per 

circular  mil-foot  at  the  temperature  corre- 

sponding to  the  rise  T; 
a  =  cross-sectional  area  of  conductor,  circ.  mils. 

The  rate  of  dissipation  of  heat  cannot  be  expressed 
by  any  exact  equation  because  heat  is  dissipated  by 
conduction,  convection  and  radiation,  and  these 
methods  of  heat  dissipation  are  not  susceptible  of 
exact  expression. 

It  is  usual  to  assume  the  dissipation  of  heat  to  be 
entirely  effected  by  one  method,  either  radiation  or 
conduction,  the  former  being  nearly  correct  for  bare 
conductors  and  the  latter,  for  insulated  cables  in 
ducts. 

Assuming  heat  dissipation  by  radiation  and  using 
Newton's  law  of  cooling, 


where  KI  is  a  constant  depending  upon  the  size  and 
style  of  conductor. 

Assuming  heat  dissipation  by  conduction, 


+aT' 

where  K2  is  a  constant,  and 

i 


286  ELECTRIC   POWER  CONDUCTORS 

t  being  the  initial  temperature.  This  is  based  upon 
the  assumption  that  the  thermal  resistivity  and 
outside  temperature  of  the  heat  insulator  surround- 
ing the  conductor  are  constant. 

The  best  experimental  data  available  is  that  of 
Fisher,  Ferguson,  and  Kennelly,  but  their  results 
do  not  exactly  agree  with  any  formula  available. 
The  author  has  therefore  adopted  the  simplest 
formula,  namely,  that  based  upon  dissipation  propor- 
tional to  the  temperature  rise,  and  has  derived  his 
.constants  so  as  to  include  all  the  best  experimental 
data  within  his  knowledge. 

The  formula  is  as  follows: 

Let 

A  =  cross-sectional  'area  of  conductor,  sq.in.; 
/  =  amperes  ; 

C  =  circumference  of  conductor,  inches; 
W=  watts     dissipated    per    sq.in.    of    surface    per 

degree  C.  temperature  rise; 
T  «=  temperature  rise,  degree  C. 
r  =  specific    resistance    of    conductor,     ohms    per 
inch  cube  at  the  temperature  corresponding  to  the 
rise  T. 

Then  in  an  inch  of  conductor, 


Watts  generated  =/2-, 
A. 

Watts  dissipated  =CWT. 


APPENDIX  II  287 

•  * 

Hence, 


or 


By   changing    the    constants    to    a   more   practical 
form,  the  formula  of  p  46  is  obtained. 

The  Short-Period  Carrying  Capacity  of  Cables.  The 
watts  generated  in  a  cable  on  account  of  its  ohmic 
resistance  are  partly  absorbed  by  the  cable  and 
partly  dissipated  from  it. 

The  joules  absorbed  when  the  temperature  is  raised 
D°  F.,  equal  pD,  where  £  =  1055  [(specific  heat 
of  conductor  X  its  weight  in  pounds  per  foot)  + 
(specific  heat  of  insulation  X  its  weight  in  pounds  per 
foot)].  Hence,  the  watts  absorbed  equal 

dD 

hr 

t  being  the  time  in  seconds. 

The  watts  dissipated  per  foot  of  cable  when  the 
temperature  rise  is  D°  F.,  are  equal  to 


q  being  the  watts  dissipated  per  foot  per  degree  tem- 
perature rise, 


288  ELECTRIC  POWER  CONDUCTORS 

Then,  if  W  =  watts  generated  per  foot  of  cable, 
W  =  watts  absorbed  +  watts  dissipated 

dD 


The  temperature  of  the  cable  rises  until  the  watts 
dissipated  equal  the  watts  generated,  so  that  when 

D  =  Fy  the  final  temperature  rise, 


or 

F-E. 

q 

Equation  (i)  may  then  be  written 

.  w,t™+D.F 

q      qdf 
whence, 

dt     p       i 


dD    q  F-Dy 

*->       " 


q  F-D' 

—  lo? 

q   10%«F- 


The  F  in  the  numerator  is  the  constant  of  inte- 
gration and  is  determined  from   the  condition  that 

W 
when  D  =  o,  t  must  be  zero.     As  F=  —  and  W=Pr. 


APPENDIX  II  289 

•   * 

where  r  is  the  resistance  of  the  cable  in  ohms  per 
foot, 

'4 

and 

F 


which  is  a  constant  and  may  be  called  G. 
Substituting  —  for  -,  equation  (2)  becomes 


Zlog---  .....     (3) 

Reducing  to  minutes,   replacing  p  by  P,  which  is 

—  —  ,    and   substituting    common   logarithms   for  the 

I055 

Naperian, 

GP  1      /       GP\  .  . 

2  =  40.5-—  log  (^  i--—  j.     ...     (4) 

Writing  Z  for  the  logarithm,  the  equation  becomes, 

'=40.5—  z  ......    (5) 

The  above  deduction  is  based  on  the  assumption 
that  r  is  constant.  As,  however,  r  varies  with  the 
temperature,  the  time  t  will  be  proportional  to  the 

mean  value  of  -.     Hence,  we  write, 


290  ELECTRIC  POWER  CONDUCTORS 

where  A  is  the  cross-sectional  area  in  circ.  mils  and  K 
is  the  mean  of  the  reciprocal  of  the  ohms  per  mil- 
foot  over  the  temperature  range  considered.  Hence, 
equation  (5)  reduces  to 

t  =  4o.$PAKGZ  ......     (6) 

The  equation  considered  above  connects  the  vari- 
ables /  and  /,  D  being  constant.  The  same  equation, 
however,  may  be  used  to  express  the  relation  between 
/  and  D,  I  being  maintained  constant,  and  for  this 
purpose  is  most  conveniently  written 


where  Z  =logio(  i  —  y;  j  and  F  is  the  final  temperature 

rise  with  /  amperes  applied  indefinitely. 

Experiments  on  the  time  element  of  fuses  by 
Schwartz  and  James,  detailed  in  the  Journal  of  the 
Institution  of  Electrical  Engineers,  July,  1908,  p.  71, 
may  be  accurately  represented  by  this  equation, 
although  a  range  of  180°  F.  is  covered.  Thus,  with 
an  enclosed  fuse  consisting  of  a  No.  27  S.  W.  G. 
copper  wire  surrounded  by  Calais  sand  in  a  J-inch 
fiber  tube,  the  temperature  rise  is  represented  by 


the  current  being  20  amperes. 

.    (From  an  article  by  the  author  in  the  Electrical 
World,  1908.) 


APPENDIX  III 
THICKNESS  OF  RUBBER  INSULATION 

The  thickness  of  insulation  to  be  placed  on  a  wire 
is  governed  by  three  features: 

1.  Errors  in  size  of  wire,  eccentric  situation  of  wire 
in  the  insulation,  and  similar  irregularities. 

2.  Insulation  not  to  be  strained  by  application  of 
test  voltage. 

3.  Insulation  to  be  thick  enough  to  have  mechanical 
strength. 

ERROR  THICKNESS 

The  thickness  of  insulation  required  to  make  up 
for  errors  and  irregularities  of  manufacture  may  be 
termed  the  "  Error  Thickness."  This  quantity  can  be 
determined  in  only  one  way  and  that  is  by  observa- 
tion. 

The  Rubber-Covered  Wire  Engineers'  Association 
have  adopted  the  following  values  in  which  the  error 
thickness  depends  only  upon  the  size  of  wire  and  not 
upon  the  thickness  of  insulation. 

The  error  thickness  used  in  the  N.  Y.  C.  R.  R. 
specification  are  based  partly  upon  the  Rubber- 

291 


292 


ELECTRIC   POWER  CONDUCTORS 


Covered  Wire  Engineers'  Association  values  and  partly 
upon  a  series  of  measurements,  a  curve  being  plotted 
through  the  mean  of  the  numerous  points  obtained. 

TABLE  I 

ERROR  THICKNESS  USED  IN  SPECIFICATIONS  OF  RUBBER- 
COVERED  WIRE  ENGINEERS'  ASS'.N  AND    OKONITE    CO. 


Size  of  Conductor. 

Error  Thickness. 

1,000,000  to  550,000  C.M. 

3/128  in. 

500,000  to  250,000  C.M. 

2/64    in. 

4/0  to     i  B.&  S. 

3/64    in. 

2  to    7 

4/64    in. 

8  to  14 

5/64    in. 

TABLE  II 

ERROR  THICKNESS  USED  IN  N.  Y.   C.  &   H.   R.   R.  SPECIFI- 
CATIONS 


Size  of  Conductor. 

Error  Thickness, 
Inches. 

Size  of  Conductor. 

Error  Thickness, 
Inches. 

14  B.&S. 

0.018 

250,000  C.M. 

°-°53 

12 

0.020 

500,000 

0.063 

IO 

O.O22 

750,000 

0.070 

8 

0.025 

1,000,000 

0.075 

6 

0.028 

1,250,000 

0.080 

4 

0.032 

1,500,000 

0.083 

2 

0.036 

1,750,000 

0.086 

I 

0.038 

2,000,000  cone. 

0.089 

0 

0.040 

2,000,000  rope 

0.095 

00 

0.042 

000 

0.045 

0000 

0.047 

APPENDIX  III  293 


Some  engineers  believe  that  the  error  thickness 
depends  upon  the  thickness  of  insulation,  being 
greater  for  heavily  insulated  cables  than  for  those 
lightly  insulated.  A  series  of  measurements  to  eluci- 
date this  point  gave  uncertain  results. 

DIELECTRIC  STRESS 

When  a  high  potential  is  established  across  the 
insulation  of  a  cable,  the  insulation  is  subjected  to  a 
strain  which  depends  upon  the  degree  of  concentra- 
tion of  electric  force.  When  this  concentration  reaches 
a  certain  value,  the  insulation  will  no  longer  be  able 
to  stand  the  strain  and  will  break  down.  It  will  not 
necessarily  be  punctured,  but  will  be  disintegrated 
only  where  the  concentration  of  electrical  force  has 
been  excessive.  For  purposes  of  analysis,  it  is  usual 
to  represent  the  intensity  of  electric  force  by  the 
density  of  imaginary  lines  of  force  stretching  radially 
from  wire  to  sheath. 

Let  F  =  dielectric  stress  in  kilovolts  per  inch  ; 
V  =  test  potential,  kilovolts  ; 
/-thickness  of  insulation,   inches,   over  error 
thickness. 


Then 


V 

F=  — ,  for  a  uniform  static  field  of  force. 


294  ELECTRIC  POWER  CONDUCTORS 

The  field  of  force  around  a  cylindrical  wire,  how- 
ever, is  not  uniform,  the  lines  extending  radially 
from  the  wire  to  the  outside  of  the  insulation.  The 
density  of  the  force  lines  is  therefore  greater  at  the 
surface  of  the  wire  than  at  the  outside  of  the  insula- 
tion. This  explains  the  well-known  fact  that  small 
wires  insulated  for  high  potentials  often  show  a  dis- 
integration of  the  inner  layers  of  insulation  without 
any  visible  defect  on  the  outside.  In  this  case 


77- 


.434  V 


! 
rlog 


where  r  is  the  radius  of  the  wire,   inches,   and  the 
logarithm  is  to  the  base  10. 
This  gives 

V  =  2.3026  Fr  log  -  — . 


This  is  not  strictly  true  for  stranded  cables,  the 
dielectric  stress  being  from  1.23  to  1.46  times  the 
value  given  by  the  above  formula. 

The  smaller  value  holds  for  thick  insulation  and 
the  latter  for  very  thin  insulation. 

(The  exact  formula  for  stranded  cables,  according 
to  Professor  Levi-Civita,  is  given  by  E.  Jona  in  the 
Transactions  of  the  International  Electrical  Congress 
at  St.  Louis,  1904.) 


APPENDIX  III 


295 


For  stranded  cables,  therefore, 

.434  V  .585  V 


F-I.34SX 


,      (<+')        ,      (t+r) 

r  log  - r  log  - 


(The  figure  1.345  is  the  mean  of  1.3  and  1.46.) 


MECHANICAL  THICKNESS 

The  error  thickness  and  the  electrical  thickness  of 
insulation  are  often  insufficient  for  mechanical  reasons. 
Table  III  shows  the  minimum  thickness  of  insulation 
which  is  permitted  by  mechanical  considerations. 
The  thickness  of  the  insulation  on  a  cable  should 
never  be  less  than  the  value  given  in  this  table,  irre- 
spective of  what  voltage  it  is  designed  for.  This 
table,  while  based  on  average  practice,  may  not 
meet  the  requirements  of  some  engineers,  and  should, 
therefore,  be  carefully  examined  before  it  is  used. 

TABLE  III 


Diameter  of 

Mechanical 

Diameter  of 

Mechanical 

Conductor, 

Thickness, 

Conductor, 

Thickness. 

Inches. 

64th  Inch. 

Inches. 

64th  Inch. 

.0 

3 

I  .2 

9 

.2 

4 

1.4 

10 

•  4 

5 

1.6 

ii 

.6 

6 

1.8 

12 

.8 

7 

2.0 

13 

I.O 

8 

296  ELECTRIC  POWER  CONDUCTORS 

INSULATION  RESISTANCE 

The   insulation   resistance   of   a   cable   is   derivable 
from  the  following  formula: 


where  M  =  megohms  per  mile  ; 

5  =  specific  resistance  in  megohms  per  inch  cube  ; 
T  =  thickness  of  insulation,  inches; 
r=  radius  of  wire,  inches; 
logarithm  is  to  base  10. 

This  formula  is  sometimes  written 


where  AT  =  58X  io~7xS. 

The  value  of  K  varies  from  870  to  23,200  for  5  =  150 
and  5  =  4000,  respectively.  The  use  of  K  instead  of 
5  has  the  advantage  of  brevity  and  is  endorsed  by 
the  manufacturers. 

In  calculating  insulation  resistance,  the  total  thick- 
ness of  insulation  should  be  used. 

EXAMPLE  OF  CALCULATION 

It  is  desired  to  find  the  thickness  of  insulation  for 
a  cable  to  be  tested  for  15  kilo  volts  (using  a  stress  of 
127  kilovolts  per  inch),  the  size  being  No.  4-0  B.  and  S. 
stranded. 


APPENDIX  III  297 

•  * 

Using  the  formula 

z,        .585^ 


we  obtain 


Inserting  the  figures, 


log  (t  +  r)  ='---  —  —-flog.  23  =1.662. 

I27X.23 


The  error  thickness  from  Table  III  is  .047  ;  hence 
the  total  thickness  of  insulation  is 

18  . 

.2  29  +  .047  =.276  =  —  in. 
64 

In  the  above  case  the  thickness  is  well  above  the 
amount  required  for  mechanical  strength,  which 
would  be  about  G/64  inch.  If  the  thickness  had 
worked  out  to  an  amount  less  than  is  required  for 
mechanical  strength,  the  proper  thickness  would 
have  to  be  taken  from  Table  III. 

In  such  cases  the  error  thickness  has  to  be  calcu- 
lated and  subtracted  from  T  in  order  to  obtain  /, 
for  which  the  test  voltage  is  calculated. 

The  table  on  p.  84  is  calculated  by  the  above 
method,  using  a  dielectric  stress  of  57  kilo  volts  per 
inch  for  the  working  voltage. 

The  cables,  therefore,  normally  operate  with  a 
factor  of  safety  of  7,  assuming  a  breakdown  stress  of 
400  kv.  per  in.  The  actual  factor  of  safety  is  liable 


298 


ELECTRIC  POWER  CONDUCTORS 


to  be  much  below  this,   as  some  brands  of  rubber 
compound  have  a  very  low  dielectric  strength. 
The  megohms  per  mile,  assuming  K  =  4000,  are 

•377 


M  =  4000  log 


23 


=  4oooX  .421  =  1684. 


ONE   INCH   IN    FRACTIONS   AND   DECIMALS 


64th. 

32nds. 

1  6th. 

8ths. 

4ths. 

Decimal. 

64th. 

32nds. 

1  6th. 

8ths. 

4ths. 

Decimal. 

I 

o.oi  <;625 

33 

l6J 

O    '?IC162CI 

2 

I 

0.031250 

74 

17 

o  ^12^0 

l£ 

o  04687"; 

3^ 

I7t 

O    C4687^ 

4 

2 

I 

0.062500 

36 

18 

Q 

O    C62C-OO 

c  • 

2* 

o  07812^ 

37 

i8i 

o  ^7812? 

6 

o  0037  =co 

38 

10 

O     C.Q77C.O 

7 

sJ 

o.  10037^ 

30 

iql 

o  60037^ 

8 
o 

4 
4* 

2 

I 



0.125000 
o  140625 

40 

41 

20 

20* 

10 

5 

.... 

0.625000 

O    6406  2  C, 

10 

c 

o.  1  5562^0 

42 

21 

o  6=;62c,o 

1  1 

^* 

o  1  7187  ^ 

43 

2ll 

o  67187=; 

12 

6 

•2 

o  '187^00 

44 

22 

1  1 

o  687500 

13 

6J 

o.  203121; 

4C 

22* 

o  703121; 

14 

7 

o  218750 

46 

23 

o  7187^0 

jc 

7l 

o  234371; 

47 

23* 

O    73437< 

16 
17 

8 
8* 

4 

2 

i 

o.  250000 
o  26^62^ 

48 

40 

24 
24* 

12 

6 

3 

0.750000 
o  76^62^ 

18 

Q 

o.  281250 

CQ 

25 

o  78i2!;o 

10 

oi 

o  206875 

CT 

2<* 

o  70687  < 

20 

10 

c 

O    712  ^OO 

C2 

26 

I  3 

o  812500 

21 

10* 

o  32812^ 

C2 

26* 

0.828125 

22 

1  1 

o  3437^0 

"?4. 

27 

o  8437^0 

23 

Ili 

O    7  ^037  s 

ce 

27* 

o  8^037"; 

24 
2C 

12 
12* 

6 

3 

.... 

0.375000 

o  30062^ 

56 

ej 

28 

28* 

14 

7 

.... 

0.875000 
o  800625 

06 

13 

o  4062^0 

58 

20 

o  0062^0 

27 

13* 

o  42187^ 

CQ 

2O* 

o  02187^ 

88 

14. 

7 

o  437^00 

60 

3O 

I  c 

o  o'?7:;oo 

2Q 

I4* 

o  4^3121; 

61 

30* 

o  0^3121; 

•7Q 

I  c 

o  4687^0 

62 

31 

o  0687^0 

21 

15* 

o  484.37^ 

63 

3ii 

o  08437^ 

32 

16 

8 

4 

2 

0.500000 

64 

32 

16 

8 

4 

I.OOOOOO 

APPENDIX  IV 

BASIS  OF   DIRECT  AND  ALTERNATING 
CURRENT  TRANSMISSION  FORMULA 

BASIS  OF  DIRECT-CURRENT  FORMULAE 

Most  Economical  Distribution  of  Copper.  The  formula 
for  the  most  economical  distribution  of  copper  is 
derived  as  follows: 

The  current  decreases  uniformly  from  the  station 
to  the  end  of  the  line,  where  a  drop  of  V  volts  is  to 
be  allowed.  Required  to  find  the  arrangement  which 
will  give  this  drop  with  the  minimum  amount  of 
copper : 

(i)  Divide  the  line  into  a  number  of  short  pieces 
of  length  /. 

The  current  in  the  first  section  from  the  far  end 
=  a/,  in  the  second  section  2a/,  in  the  third,  ^al,  and 
so  on,  where  a  =  amperes  taken  from  the  line  per  foot 
of  length. 

The  volume  of  copper  in  the  first  section  may  be 
called  yj,  in  the  second  y^l,  in  the  third  y^l,  and  so 
on,  these  quantities  being  c.m.-ft. 


300  ELECTRIC  POWER  CONDUCTORS 

The  resistance  of  the  first  section  is  —  —  •  Z,  of   the 

y\ 

second  —  —  •/,  of  the  third  -  —  ~/,  etc.,  where  IO.E;  is 
y2  y* 

the  ohms  per  mil-foot. 

The  drop  in  the  first  section  is   io.5a/2  —  ,  in  the 

yi 

9  2 

second  io.5a/2  —  ,  in  the  third,  io.5a/2  —  ,  etc. 


The  total  copper  =  l(y\  +  y2  +  y$  +  ,  etc.). 
Total  drop  =  i  o.  sal2  (—  +  —  +  —  +  ,  etc.  ). 

\3;i    y2    ys 

It  is  required  to  make  l(y\  +^'2+^3  +  ,  etc.)  a  mini- 
mum subject  to  the  condition  that/  --  1  ---  h  —  +  ,  etc.) 

Vxi    y2    y*          / 

shall  be  a  constant. 

Multiply  the  latter  series  by  a  constant  P  having 
the  dimensions  of  a  length  to  the  fourth  power  and 
add  the  two  series.  The  following  one  is  obtained: 


P         \      /2P          \      l$P          \ 

-  +  y\  )  +  -  -  +  y*  )  +  (-  •  +  y*  +  ,  etc. 

i        I     \y2        /     \ys        / 


The  series  l(yi  +^2  +  ^3  +  ,  etc.),  is  a  minimum  when 
the  above  series  is  a  minimum.  This  occurs  when 
the  differential  coefficient  of  each  term  with  regard 


APPENDIX  IV  301 

•  * 

to  its  y  is  zero.      Hence  differentiating  and  equating 
to  zero, 


etc.  =o. 
nP 


Now,  w/  is  x,  the  distance  from  the  far  end,  and  / 
is  a  constant. 

IP 


Hence,  y  =  \—Vx. 

IP 
The  value  of  the  constant  \—  must  be  found.     The 

drop  in  dx,  which  may  be  called  dv,  equals  current 
at  distance  x  from  the  end  multiplied  by 

10.5  -dx 


c.m.  at  that  distance' 
Hence, 


ax-  x  =  io.$a--=-x  =  10.50 


--^=-dx  =  10.50  v^^/x-dx, 

P  Vx 


A     - 


2  A      /—        /- 

y=-  Xio.5—  VL-  Vx. 


302  ELECTRIC  POWER  CONDUCTORS 

This  equation  gives  a  parabola  of  circular  mils 
that  represents  the  most  economical  distribution  of 
copper  with  uniform  drain  of  current. 

This  deduction  is  based  upon  a  modification  of  the 
"Method  of  Undetermined  Multipliers"  given  in 
Chapter  XI  of  Williamson's  "Differential  Calculus." 


FIG.  69, 

Resistance  with  Infrequent  Cross-Bonding.      Referring 
to  Fig.  69,  the  following  additional  notation  is  used: 

R=  equivalent  resistance  of  load; 


D-f+g+k. 

Using  Maxwell's  method  of  imaginary  currents  the 
following  four  equations  are  obtained: 

An  -«3  -/u  +IRi=E 

Fi2  —  dis  —  gi±  —IR  =  —E 
—  ci\  —di2  +Bis  =o 

—fii  —gi<2  +Di4:  =o 

fl      -«2  =/ 


APPENDIX  IV 


303 


Then,  using  determinants 


R 


A  o    -c    -f  E 

0  F  -d    -g  -E 
-c  —d       B       o  o 
-f  —g        o        D  o 

1  —  i        o        o  I 


A       o    -c     -f        I 

0  F  —d    —g    —I 
—c     —d       Boo 
-f     -g        o        Do 

1  —  i        o        o        o 


R  having  been  obtained  by  solving  the  above  deter- 
minant, is  used  in  the  following  formula,  in  which  % 
is  the  resistance  from  the  load  to  the  two  stations  in 
multiple : 

,.f-* 

E 
As  the  expression  for  R  contains  —,  this  quantity 

cancels  out,  leaving 


DB 


304  ELECTRIC  POWER  CONDUCTORS 

By  making /  =  o,  g  =  o,  and  /*  =  oo, 


B 

x  —  •— ™— — -^— ^ 


which  is  the  formula  given  on  p.  121  with  somewhat 
different  notation. 

The  formulas  for  x  and  R  given  on  p.  122  are 
obtained  by  differentiating  R  with  respect  to  x, 
equating  to  zero  and  rearranging  the  terms. 


BASIS  OF  ALTERNATING-CURRENT  FORMULA 

With  the  exception  of  the  problem  of  determining 
the  size  of  wire  to  use  for  a  given  pressure  drop, 
the  solution  in  each  case  is  given  directly  by  means 
of  a  comparatively  simple  formula;  in  the  particular 
case  of  determining  the  size  of  a  wire  for  a  given 
drop,  an  approximation  is  first  obtained  and  then 
the  error  involved  in  the  approximation  determined, 
which  error,  however,  will  be  found  negligable  in 
most  practical  cases.  Moreover,  the  use  of  this 
particular  approximate  formula,  followed  by  a  deter- 
mination of  the  error  involved,  has  a  distinct  advan- 
tage, since  a  large  error  immediately  indicates  that 
the  drop  for  any  size  of  wire  within  a  wide  range  will 
differ  only  slightly  from  the  permissible  drop  given, 


APPENDIX  IV  305 

and  that  therefore,  either  by  allowing  a  slight  increase 
in  the  drop,  or,  if  this  is  not  feasible,  by  employing 
two  separate  circuits  instead  of  one,  a  very  consider- 
able saving  in  copper  can  be  effected. 

The  formulas  given  are  all  readily  derived  from  the 
usual  diagram  of  two  impedances  in  series,  namely, 
the  impedance  of  the  load,  and  the  impedance  of 
the  line,  remembering  that  the  ratio  of  power  lost 
to  power  delivered  is  equal  to  the  ratio  of  line  resist- 
ance to  load  resistance,  and  that  the  ratio  of  the 
pressure  at  the  generating  end  to  the  pressure  de- 
livered is  equal  to  the  ratio  of  the  total  impedance  to 
the  load  impedance. 

The  reactance  tables  are  based  upon  the  fact  that 
the  reactance  of  a  wire  for  a  given  frequency  can  be 
considered  as  the  sum  of  two  quantities,  one  varying 
only  with  the  spacing  of  the  wires  and  the  other  only 
with  the  size.  The  resistances  have  been  calculated 
for  copper  of  98%  conductivity  and  for  aluminum 
of  62%  conductivity  (Matthiessen's  standard,  i.e., 
one  meter- gram  of  soft-drawn  copper  =  0.141729  in- 
ternational ohm  at  o°  C.),  both  at  20°  C.,  plus  an 
increase  of  i%  on  account  of  stranding,  temperature 
coefficient  0.42%  per  degree  C.  The  weights  given 
are  the  weights  of  solid  wire  of  equal  cross-section 
increased  i%  on  account  of  stranding. 


306  ELECTRIC  POWER  CONDUCTORS 


BASIS  OF  FORMULAE   FOR  TRANSMISSION   LINE  WITH  RESIST- 
ANCE, REACTANCE,  LEAKAGE,  AND  CAPACITY 

(H.  FENDER.) 

Let  i  =  instantaneous  value  of  current  at  time  /  ; 
V  =  instantaneous  value  of  difference  of  poten- 
tials between  wire  and  neutral  at  time  t\ 
1  =  distance  from  load  to  the  point  where  current 

and  voltage  are  being  considered; 
C  =  capacity  of  each  line  wire  to  neutral; 
L  =  inductance  of  each  line  wire  ; 
g  =  leakage  susceptance  per  line  wire; 
r  =  resistance  per  line  wire. 

The  formulae  are  derived  from  the  following  differ- 
ential equations  : 


dV  di 


from   which   can   be   derived   by   differentiation   the 
following  differential  equations  of  the  second  order: 

d2i         .  di 

-=gn  +  (CV+Lg)- 

dV 


APPENDIX  IV  307 

•   * 

These  equations  are  of  the  form 


and  are  satisfied  by  the  integral  relation 
=  Aekx  cos  (wt  +  hx  —  a). 


The  various  constants   can  be  found  by  substitut- 
ing this  integral  in  the  differential  equations. 


APPENDIX  V 
BASIS  OF  FORMULA  FOR  STRESSES  IN  SPANS 

THE   approximate  equations  for  a  wire  suspended 
between  two  points  are 


2r 

r       8  / 
L  = 


where  D  =  deflection  of  wire  at  center  of  span  in  feet 
in  the  direction  of  the  resultant  force  at 
temperature  t\ 

L  =  length  of  wire  at  temperature  /  under  ten- 
sion T\ 

p  =  ratio  of  the  resultant  of  weight  of  wire  and 
sleet  and  the  wind  pressure  to  weight  of 
wire ; 

m=  weight  of  conductor  per  cubic  inch; 
/  =  length  of  span,  feet; 

pl 


APPENDIX  V  309 


* 


Letters  with  subscript  zero  refer  to  corresponding 
quantities  at  temperature  fo  and  tension  TQ.     Hence, 


The  relation  between  the  length  L  of  wire  at  tem- 
perature /  under  tension  T  to  length  Lr  at  zero  tem- 
perature and  unstressed,  is  given  by  the  equation, 


Similarly, 


where  a  is  the  coefficient  of  expansion  per  degree. 
Combining  the  last  four  equations  and  neglecting 

cross  products  of  the  term  6m2 K2,  — ,  and  at,  since 

these  quantities  are  of  the  order  of   io~3  or  less  in 
any  practical  case,  we  get  the  following  expression, 


The  graphical  method  is  based  upon  the  above 
formulas,  the  equations  of  the  curves  being  given  in 
Chapter  IV. 


APPENDIX  VI 
EXPLANATION  OF  SPECIFICATIONS 

i.    CABLES  FOR  AERIAL  LINES 

SOLID  conductors  are  only  used  for  the  smaller 
sizes,  say  up  to  No.  o  B.  and  S.,  seven  strands  being 
used  up  to  250,000  c.m.  and  a  larger  number  for 
sizes  above  that. 

The  total  effective  area,  of  copper  is  that  of  the 
sum  of  the  individual  wires  laid  out  straight  and 
measured  at  right  angles  to  their  axes,  because  the 
current  follows  the  spiral  of  the  cable  without  appre- 
ciably passing  from  one  strand  to  another. 

The  pitch  is  important  on  account  of  its  effect 
upon  the  tensile  strength  of  the  cable  (see  p.  17). 

Pounds  per  square  inch  at  the  elastic  limit  divided 
by  the  elongation  expressed  as  a  decimal  fraction  gives 
the  modulus  of  elasticity. 

The  object  of  the  "  flexibility  "  test  is  to  assure 
the  possibility  of  making  Western  Union  joints  with 
solid  conductors  and  to  assure  the  absence  of  undue 
stresses  in  strands.  Theoretically,  the  wrapping  test 
should  be  performed  at  the  lowest  temperature  to 

310 


APPENDIX  VI  311 

-  * 

which  the  wire  will  be  exposed  in  practice,  but  the 
lowest  temperature  conveniently  attainable  is  32°  F., 
which  is  accordingly  specified. 

The  permissible  excess  of  area  is  limited  in  order 
to  prevent  the  manufacturer  obtaining  the  specified 
conductivity  and  strength  by  using  more  metal.  This 
is  often  done  where,  as  is  usually  the  case,  the  cable 
is  sold  by  the  pound,  and  should  be  avoided,  not  only 
on  account  of  the  extra  expense,  but  also  on  account 
of  the  decreased  strength  of  the  wire  per  square  inch. 

2.    INSULATED  CABLE 

General.  It  is  advisable  to  state  the  conditions 
under  which  the  cable  is  to  be  used  in  order  that 
the  manufacturer  may  run  no  chance  of  misunder- 
standing any  part  of  the  specifications,  thereby 
producing  a  cable  unsuitable  for  the  purpose  for 
which  it  is  intended  to  be  used.  Furthermore,  it 
gives  the  manufacturer  an  opportunity  to  judge 
which,  of  several  products  fulfilling  the  specification, 
is  best  suited  to  the  conditions. 

Form  of  Cable.  Soft-drawn  copper  is  almost  uni- 
versally used  for  insulated  conductors  in  preference 
to  the  hard-drawn  product,  on  account  of  its  com- 
parative cheapness  and  its  superior  flexibility  and 
conductivity.  Hard-drawn  copper  is,  however,  used 
for  special  work,  such  as  long  spans  of  insulated  wire. 

Solid  wire  may  be  used  where  flexibility  is  of  little 


312  ELECTRIC  POWER  CONDUCTORS 

importance  but  for  larger  sizes  than  No.  10  B.  and  S. 
stranded  conductors  are  desirable  if  they  have  to  be 
drawn  into  conduits.  Conductors  of  2,000,000  c.m. 
area  and  over  are  inconveniently  stiff  even  in  the  form 
of  concentric  cables  and  are  therefore  often  rope-laid. 

Two  conductor  cables  of  oval  form  contain  less 
lead  and  filling  than  round  ones,  and  are  therefore 
preferred  on  account  of  their  cheapness. 

The  lateral  fillings  not  only  serve  the  purpose  of 
making  the  cable  mechanically  solid,  but  also  to 
prevent  static  discharges  between  the  insulation  and 
the  lead;  such  discharges  arising  from  the  steep 
potential  gradient  in  the  air  spaces  due  to  the  low 
specific  inductive  capacity  of  air  compared  with  that 
of  the  insulating  compound. 

Multiple  conductor  cables  being  generally  com- 
posed of  small  wires  furnished  with  'sufficient  insu- 
lation for  their  individual  mechanical  protection, 
require  some  further  protection  on  account  of  their 
greater  size  and  consequent  liability  of  injury  in 
handling.  For  this  reason  a  covering  of  tarred 
rope  is  advised. 

The  object  of  one  conductor  differently  colored 
from  the  others  is  to  facilitate  the  identification  of 
wires  at  the  opposite  ends,  care  being  taken  in  splic- 
ing to  first  join  the  ends  of  the  marked  wires,  and 
then  join  the  others  in  their  natural  order. 

A  final  insulating  belt  over  the  rope  serves  prin- 
cipally to  hold  the  wires  and  ropes  together  and 


APPENDIX  VI  313 

to  give  a  smooth  surface  to  the  lead  or  braid  cover- 
ing. This  is  very  important  with  lead,  as  a  pro- 
jection on  the  inner  surface  of  the  sheath '  greatly 
reduces  the  dielectric  strength  of  the  cable. 

Conductors.  While  soft  drawn  copper  of  over 
100%  Matthiessen's  standard  is  obtainable,  the 
manufacturers  have  difficulty '  in  producing  it 
steadily,  and  therefore  charge  an  abnormal  price 
for  it;  98%  conductivity  is  about  the  best  com- 
mercially obtainable. 

Rubber  insulation,  owing  to  its  sulphur,  attacks 
copper,  which  must  therefore  be  protected  by  a 
coating  of  metal  not  affected  by  sulphur.  Var- 
nished cambric  also  affects  copper  when  certain 
chemicals  are  used  in  the  preparation  of  the  oils, 
and  therefore  requires  a  separator  like  rubber. 
Either  tin  or  unvulcanized  rubber  containing  no 
sulphur  is  used  for  this  purpose. 

In  stranded  conductors  the  major  part  of  the 
current  follows  the  spirals  of  the  strands.  The 
increase  of  copper  area  due  to  spiralling,  therefore, 
has  no  effect  in  reducing  the  resistance,  and  the 
effective  area  of  copper  is  the  combined  area  of 
the  strands  when  laid  out  straight  and  measured 
at  right  angles  to  their  axes. 

Insulation.  Many  engineers  leave  the  thickness 
of  insulation  to  be  determined  by  the  manufacturers 
from  the  specified  tests.  This  practice  has  the 
disadvantage  of  permitting  the  various  competing 


314  ELECTRIC  POWER  CONDUCTORS 

manufacturers  to  present  bids  based  on  different 
factors  of  safety  with  the  results  that  all  the  manu- 
facturers will  use  as  little  insulation  as  possible 
and  that  the  lowest  bidder  will  probably  be  the  one 
who  is  using  the  lowest  safety  factor.  If,  on  the 
other  hand,  the  insulation  thickness  is  specified, 
the  manufacturer  who  produces  a  compound  of 
higher  dielectric  strength  than  his  competitors  is 
reduced  to  an  equality  with  them,  and  the  buyer 
loses  an  opportunity  of  obtaining  the  cheapest 
product.  This  objection,  however,  is  of  little  weight 
at  the  present  time,  as  little  difference  exists  in  the 
dielectric  strength  of  different  makes  of  paper  and 
cambric  insulation,  and  rubber  is  seldom  used  under 
high  dielectric  stress. 

Taping  and  Braiding.  Rubber  insulation  cannot 
be  properly  vulcanized  without  a  covering  of  tape. 
The  majority  of  manufacturers  vulcanize  in  a  tape 
which  becomes  a  permanent  part  of  the  insulation, 
but  some  vulcanize  in  a  temporary  tape  of  tin-foil 
or  other  non-adhesive  material  and  put  the  per- 
manent tape  on  the  cold,  vulcanized  insulation. 
In  either  case,  the  tape  serves  as  a  mechanical 
protection  by  giving  a  hard  surface  to  the  insula- 
tion, but  its  principal  function  in  lead-sheathed 
cables  is  to  protect  the  surface  of  the  insulation 
from  being  burned  in  the  lead  press. 

Successive  turns  of  the  tape  should  overlap,  but 
the  overlap  should  be  less  than  half  the  width  of 


APPENDIX  VI  315 

•   * 

the  tape,  in  order  to  avoid  ridges  where  turns  would 
be  superimposed.  On  the  other  hand,  the  overlap 
should  be  sufficient  to  insure  protection  when  the 
cable  is  bent  to  a  sharp  radius. 

Braiding  is  simply  a  cheap  sheathing  for  cables 
to  be  used  in  dry  places  or  where,  for  any  other 
reason,  lead  cannot  be  used.  Six-lea  hemp  is  hemp 
yarn  having  six  times  300  yards  to  the  pound,  a 
lea  of  hemp  being  300  yards. 

Sheath.  Pure  lead  is  too  soft  for  sheathing,  but 
alloyed  with  a  small  quantity  of  tin  it  has  excellent 
mechanical  properties.  Two  per  cent  of  tin  is  found  to 
be  ample  for  this  purpose,  a  greater  quantity  having 
the  effect  of  rendering  the  metal  liable  to  crystallize. 

Armor.  Armor  is  used  either  as  a  substitute  or 
as  a  protection  for  sheathing. 

When  used  as  a  substitute  it  is  usually  in  the 
form  of  a  galvanized  steel  tape.  It  is  used  where 
cables  are  exposed  to  vibration  which  would  crystal- 
lize the  sheath  metal. 

Armor  is  used  as  a  protection  for  sheathing  on 
submarine  cables,  and  on  cables  intended  to  be 
laid  in  the  ground  without  ducts.  For  these  pur- 
poses galvanized  wire  is  preferable  to  steel  tape  owing 
to  the  possibility  of  putting  on  a  greater  thickness 
without  making  the  cable  too  stiff. 

Tests.  Cable  should  be  immersed  for  a  sufficient 
time  to  enable  the  water  to  penetrate  anywhere 
it  could  penetrate  after  the  cable  is  installed.  In 


316  ELECTRIC  POWER  CONDUCTORS 

the  case  of  rubber  or  varnished  cambric  insulation 
this  requires  from  twelve  to  twenty-four  hours,  but 
a  very  short  period  is  sufficient  for  paper  insulation 
as  it  is  very  hygroscopic. 

The  conditions  prescribed  for  the  megohms  test 
constitute  a  convenient  standard,  which  is  univer- 
sally accepted. 

Capacity  Guarantee.  Cables  of  high  electrostatic 
capacity  should  be  avoided  for  high  tension  work  on 
account  of  the  large  charging  current  they  take.  The 
proposals  should  therefore  be  scanned  with  the  view 
of  eliminating  cables  of  undesirable  capacity. 

It  is  seldom  necessary  to  initially  specify  the 
capacity,  as  the  standard  products  of  the  manu- 
facturers are  satisfactory  in  that  respect. 

Installation.  The  'responsibility  for  correct  cable 
lengths  should  be  placed  on  the  contractor  whenever 
possible,  in  order  to  avoid  troubles  arising  from 
errors  in  measurement.  Lengths  should  never  be 
estimated  from  subway  plans,  as  splicing  chambers 
can  seldom  be  built  exactly  according  to  plan. 

It  is  advisable  to  specify  the  compound  to  be  used 
in  the  sleeves  in  order  to  avoid  the  use  of  more  than 
one  kind  of  compound,  plurality  of  compounds  giving 
rise  to  trouble  in  maintenance  and  repair  work. 


APPENDIX  VI  317 


3.     THIRTY  PER  CENT  PARA  RUBBER  COMPOUND 

Description  of  Insulation.  The  object  of  specifying 
that  not  more  than  33%  of  rubber,  is  to  be  assured 
that  only  Para  rubber  is  used.  If  an  inferior  grade  of 
rubber  is  used  the  compound  will  have  to  contain 
more  than  33%  rubber  to  meet  the  test  requirements. 
As  the  permanence  of  these  inferior  grades  is  doubtful 
their  use  should  be  guarded  against.  Furthermore,  in 
the  presence  of  low  grade  rubber,  it  is  practically  im- 
possible to  determine  how  much  high  grade  rubber 
is  in  the  compound. 

The  small  amount  of  extract  in  the  gum  is  the 
essential  quality  which  differentiates  the  finest  dry 
Para  rubber  from  other  kinds.  The  small  amount 
of  volatile  extract  specified  for  the  complete  com- 
pound is  to  assure  the  absence  of  an  excess  of  volatile 
matter  which  wTould  evaporate  and  leave  the  insula- 
tion dry  and  also  to  prevent  the  over-mastication  of 
rubber  during  manufacture. 

The  amount  of  sulphur  is  limited  in  order  to  pro- 
tect the  conductors  from  corrosion. 

Tests.  There  is  some  question  about  the  proper 
electrical  properties  which  rubber  insulation  should 
possess.  From  the  operating  standpoint  a  very  low 
insulation  resistance  should  suffice,  but  it  appears 
that  a  high  insulation  resistance  is  some  indication 
of  sound  homogeneous  structure.  High  insulation 


318  ELECTRIC  POWER  CONDUCTORS 

resistance  may  be  secured,  however,  by  artificial 
means,  such  as  by  the  use  of  paraffine  wax,  and  is 
therefore  not  a  reliable  indication  of  quality. 

High  dielectric  strength  is  very  desirable  but  it  is 
often  obtained  at  the  cost  of  permanence,  it  being 
possible  to  greatly  increase  the  dielectric  strength 
by  putting  more  or  less  volatile  oils  in  the  compound. 

High  insulation  resistance  and  high  dielectric 
strength  are  each  strongly  recommended  by  different 
manufacturers,  but  their  reasons  for  doing  so  are 
more  commercial  than  technical. 

The  remarks  under  the  heading  of  tests  in  specifi- 
cation No.  2  apply  equally  to  this  specification. 
The  object  of  making  the  megohms  test  of  multiplex 
cables  before  assembling,  is  to  have  test  figures  which 
can  be  checked  by  theory,  there  being  no  way  of 
calculating  the  insulation  resistance  of  a  multiplex 
cable.  The  high  voltage  test  is  made  before  assem- 
bling in  order  to  eliminate  faulty  pieces  and  after 
assembling  in  order  to  detect  faults  which  may  have 
arisen  during  assembling. 

The  temperature  coefficient  of  insulation  resistance 
is  specified  for  two  reasons:  first,  in  order  to  prevent 
the  manufacturer  using  a  coefficient  which  will  make 
any  test  results  agree  with  the  specifications;  and 
second,  because  it  has  been  found  that  compounds 
of  high  temperature  coefficient  (i.e.,  over  3%  per 
deg.  F.)  generally  do  not  contain  30%  Para  rubber. 

The   stretch   tests    are   somewhat   arbitrary,    being 


APPENDIX  VI  319 

•  * 

founded  partly  upon  manufacturers'  recommendations 
and  partly  upon  experience  with  various  grades  of 
rubber.  While  many  excellent  compounds  entirely 
fail  to  meet  this  test,  it  cannot  be  questioned 
that,  combined  with  the  restriction  in  the  quan- 
tity of  rubber,  it  practically  bars  objectionable  com- 
pounds. 

The  paragraph  containing  temperature  limits  is 
intended  to  prevent  the  heating  and.  stretching 
of  rubber  prior  to  tests,  a  little  judicious  handling 
often  having  the  effect  of  making  a  doubtful  sam- 
ple pass. 


4.  RUBBER-COVERED  WIRE  ENGINEERS'  ASSOCIA- 
TION SPECIFICATIONS  FOR  THIRTY  PER  CENT 
RUBBER  COMPOUND 

This  specification  is  a  compromise  agreed  upon  by  the 
principal  manufacturers,  but  while  doubtless  prepared 
in  good  faith,  the  number  of  different  compounds 
which  it  is  intended  to  cover  is  so  great  that  it  will 
practically  pass  anything.  In  other  words,  this 
specification  contains  no  requirement  which  cannot 
be  met  by  all  the  manufacturers,  and  this  compre- 
hensiveness is  obtained  at  the  sacrifice  of  that  severity 
which  makes  a  specification  really  useful. 


320  ELECTRIC  POWER  CONDUCTORS 


5.    and    6.     VARNISHED  CAMBRIC  AND  PAPER 
INSULATION 

These  specifications  need  little  explanation  beyond 
the  statement  that  cambric  and  paper  being  staple 
articles  of  manufacture  of  undoubted  permanence 
and  excellent  electrical  qualities,  they  need  no  fur- 
ther specification  than  a  general  description.  The 
insulation  resistance  may  be  left  to  the  manufacturer, 
provided  that  it  is  sufficiently  high  for  successful 
operation,  but  the  voltage  test  should  be  severe. 


APPENDIX  VII 

BASIS   OF   TABLES   GIVING   SELF-INDUCTION 
OF  PARALLEL  WIRES 

IT  is  surprising  to  note  the  errors  made  by  technical 
writers  in  their  attempts  to  express  the  inductance 
of  a  pair  of  parallel  wires,  especially  since  a  very 
simple  and  accurate  formula  has  been  available  in 
most  of  the  standard  mathematical  treatises  on  elec- 
tricity from  J.  Clerk-Maxwell  to  Alex.  Russel. 

The  inductance  of  a  circuit  is  a  measure  of  the 
magnetic  energy  associated  with  the  current  in  it  and 
is  defined  by  the  well  known  equation 


where  E  is  the  energy  in  the  magnetic  field  inter- 
linked with  a  circuit  of  inductance  L,  carrying  an 
unvarying  current  i. 

This  definition  gives  rise  to  the  following  equation: 


321 


322  ELECTRIC  POWER  CONDUCTORS 

where  d  =  distance  apart  of  wires,  center  to  center; 
r  =  radius  of  wires  in  same  unit ; 
L  =  inductance  of  each  wire  in  millihenrys. 

The  formulae  given  in  Chapter  XII  are  based  upon 
the  above  equation. 

In  the  case  of  a  circuit  composed  of  two  parallel 
wires  the  size  of  which  is  negligible  in  comparison  with 
their  distance  apart,  the  inductance  is  approximately 
equal  to  the  total  flux  embraced  by  the  circuit  due  to 
the  unit  current  therein. 

This  definition,  although  based  upon  an  approxi- 
mation, is  often  assumed  to  be  exact  and  used  as 
the  basis  of  various  self-induction  formulae. 

The  flux  around  a  wire  is  plotted  from  the  well- 
known  equations 

2£ 

B  = —  outside  the  wire, 
r 

n  AW 

and  B  =-™  inside  the  wire, 

where  B  is  the  flux  density,  lines  per  sq.cm.  at  dis- 
tance; r  cms.  from  the  center  of  a  long  straight  wire 
of  radius  R  cms.  carrying  a  current  of  i  absolute 
units. 

When  two  conductors  carrying  currents  in  opposite 
directions  are  brought  into  proximity,  the  magnetic 
whirls  around  the  conductors  are  squeezed  together 
and  the  axes  of  the  two  whirls  are  pushed  away 
from  the  axes  of  the  conductors. 


APPENDIX  VII  323 

-  • 

If  the  integration  is  taken  between  the  centers  of 
wires,  a  formula  containing  the  term  log  -  -  instead 

of   log  -     will    be   obtained;    if    taken    between    the 

axes  of  the  whirls  a  very  long  and  complicated  for- 
mula is  obtained. 

One  of  these  incorrect  formulae  is  often  given  in 
text-books  as  exact,  and  the  exact  formula  derived 
from  it  as  an  approximation,  the  authors  of  these 
books  neglecting  the  fact  that  their  original  defini- 
tion involved  an  approximation. 

It  should  be  noted  that  where  only  a  part  of  a 
circuit  is  involved,  there  may  be  some  magnetic 
energy  interlinked  with  it,  but  originated  by  the 
current  in  some  other  part  of  the  circuit.  Such 
extraneous  magnetism  adds  to  the  "  flux  due  to 
unit  current,"  but  not  to  the  magnetic  energy  asso- 
ciated with  the  current  in  that  part  of  the  circuit 
under  consideration. 

The  tables  given  in  Chapter  XII  are  based  upon  the 
fact  that  the  equation  for  inductance  may  be  resolved 
into  a  sum  of  two  quantities,  one  of  which  depends 
upon  the  size  of  wire  and  the  other  upon  the  distance 
apart  of  the  wires,  a  simple  fact  first  utilized  by 
H.  Fender  and  published  in  Foster's  "  Electrical 
Handbook." 

The  fundamental  formula  given  above  may  be 
resolved  into  the  various  forms  given  below. 


324  ELECTRIC   POWER  CONDUCTORS 

Let     d  =  distance  apart  of  wires,  center  to  center; 
r  =  radius  of  wires  in  same  unit; 
L  =  self-induction  of  each  wire  in  millihenrys, 
or  thousandths  of  a  henry. 

The  logarithms  are  common,  i.e.,  to  the  base  10. 
L  per  cm.  =.000,000,5    +.000,004,605  log-. 

L  per  in.  =.000,001,27  +  .000,011,68     log—. 

L  per  ft.  =.ooo, 01 5, 24 +  .000, 140, 3       log-. 

L  per  1000  ft.     =.015,24         +.140,3  log-. 

f 

L  per  mile  =.o8q,47         +.74111  log-. 

L  per  kilometer  =  .05  +  .460,5  log 

For  magnetic  wires  the  first  constant  in  each  of  the 
above  formulae  should  be  multiplied  by  permeability 
of  the  wire.  An  average  value  of  the  permeability  for 
high  grade  iron  telegraph  wire  is  150,  which  value  has 
been  used  in  the  formulae  given  on  p.  275. 


INDEX 


PAGE 

Acetone  extract 62,  67,  189,  193,  317 

Air,  dielectric  strength 102 

Alternating  current  transmission  formulae 133,  304,  306 

Alternating  current  railway  feeder  calculations 142 

Aluminum  cable 20 

carrying  capacity 2,  3,  45 

coefficient  of  expansion  .  , ' i 

compared  with  copper i 

conductivity i,  22 

cost 3 

elastic  limit i 

melting-point 1,3 

modulus  of  elasticity i 

ohms  per  mile 137 

pounds  per  mile 140 

resistance  of  cable 137 

resistance  of  wire 27 

scrap  value 4 

specific  gravity i 

sleet  on 3 

splicing 228 

tensile  strength i,  3 

wire  resistance 27 

American  or  B.  &  S.  gauge 8,  281 

325 


326  INDEX 


American  Steel  &  Wire  Co.  gauge u 

Ampere-feet 108 

Annular  cable 43 

Armor 185,  315 

Auxiliary  feeders  for  railways m 

Auxiliary  feeders  infrequently  connected  to  contact  conductors...   119 

Ayrton,  W.  E 202,  205 

Ayrton  and  Mather  shunt 208 

Barium  sulphate  in  rubber 66 

Belted  triplex  cable 91 

Birmingham  wire  gauge 10,  1 1 

Block  and  tackle  for  cable  pulling 222 

Bonds 196,  252 

Booster 127 

Braiding 184,  314 

Branches,  drop  in 108 

Breaking  strength,  see  Tensile  strength. 
Brown  &  Sharpe  gauge:       ' 

approximate  rules  based  upon 28,  no 

basis  of 281 

combination  of  wires  of 9 

compared  with  others 1 1 

peculiarities no 

ratio  of 281 

size  of  wires  in 8 

Brush  generator  for  cable  testing 216 

Bonds,  area  of  rail  holes  for 269 

brazed 255 

cable 260 

carrying  capacity 262 

chemical  adhesion 252 

classification 252,  253 

compressed 257 

concealed 258 

efficiency  of 261 


INDEX  327 

PAGE 

Bonds,  equivalent  copper  area 264 

exposed 258 

foot 259 

head 259 

mechanical  adhesion 252,  256 

pin  expanded 257 

precautions  in  installing 264 

ribbon 260 

single  and  double 265 

soldered 253 

solid 260 

web 259 

welded 255 

Buck,  H.  W.,  on  wind  velocity 165 

Cable,  aluminum,  dimensions  and  weights 20 

copper,  dimensions  and  weights 20 

definition 13 

diameter 15,  20 

diameter  of  wires  in 19 

effective  area  of 310 

grip 220 

length  measurement 316 

number  of  wires  in 14 

resistance 19,  29,  137 

space  wasted  in 18 

specifications 1 79,  181,  310 

splicing 227,  229 

ultimate  strength 17 

weight 16,  20,  140 

Cambric  insulation,  properties 73 

specification 195,  320 

test  voltage 90 

thickness  of  insulation 90 

Capacity,  approximation  for  line 277 

effects  in  transmission  line 139,  153,  277 


328  INDEX 

PAGE 

Capacity,  guarantees 187,  316 

injurious  effects  of 277 

measurement 209 

parallel  bare  wires 278 

single  overhead  wire 279 

susceptance 141 

three-phase  cable 280 

two-conductor  cable 280 

Capstan,  for  cable  drawing 221,  223 

Carrying  capacity,  alternating  current  cables 43 

aluminum 2,  3,  45 

annular  cables 43 

basis  of  formulae 284 

chart 52 

effect  of  number  of  adjacent  cables  on 50 

intermittent 53 

lead-covered  cables  in  ducts 45 

multiple-conductor  cables 49 

short  period .* 54 

underwriters'  rules 44 

wires  of  various  metals 50 

Cast  welding 265 

Catenary,  equations  of 175 

Charging  current 278 

Christie's  bridge 200 

Circuit-breaker  house  system 120 

Circuit-breakers  to  protect  cables 245 

Circular  mil 9 

Cierk-Maxwell,  J 321 

Cloth  insulation 73 

Code  compounds 82 

Comparison  of  systems  of  distribution 105,  106 

Compound  for  cable  sleeves 232,  236 

Concentric  strand,  definition 13 

Conductivity  of  atmosphere 102 

Conduit  wiring 82 


INDEX  329 

* 

PAGE 

Connectors 228,  231,  233 

Continuous  current  systems 105,  106 

Copper  cable,  weights  and  sizes  .  .  . 140 

Copper,  hard  drawn 4 

Copper,  soft  drawn,  cable  cores 8 

mechanical  properties 5 

solid  wire,  sizes  and  weights 8 

ultimate  strength 7 

Copper  wire,  resistance 24,  25,  26,  137 

Copley,  A.  W 142 

Cost  of  energy 127 

Crocker,  F.  B ^r 

Current  density,  economical 157 

Current  value  used  in  feeder  calculations 126 

Decimal  and  vulgar  fractions 298 

Depreciation 238 

Deterioration  of  cables 240 

Determinants 35 

Dielectric  strength  of  air 102 

paper  insulation 72 

rubber  insulation 7! 

Dielectric  stress 293 

Direct  current  cables  in  service 77 

Direct  current  short  circuits 93 

Dissipation  of  heat  from  conductors 286 

Distribution  of  copper  for  economy 115,  299 

Distribution  of  railway  load 114 

Drawing  cables  in  ducts 220 

Drop  in  mains  and  branches  108 

Economical  distributi2n,  basis  of  formula  for 299 

Economy  of  conductors 156 

Economy  in  distribution ntj 

Edison,  gauge I2 

five-wire  system „ 105 


330  INDEX 

PAGB 

Edison,  three-wire  system 105 

Electrolysis 240 

Electrostatic  charges 80 

Energy  cost 127 

English  legal  wire  gauge 1 1 

Equations,  solution  of,  by  determinants 35 

Error  thickness 292 

Examples  of  transmission  calculations 146 

Factors  for  correction  of  insulation  resistance,  cambric 75 

paper 72 

rubber 65,  192 

Faults,  locating 213 

Feeder  calculations,  lighting  systems 107 

railways 115,  142 

Feeders  for  railways 1 1 1 

Fisher  loop  test 214 

Flexibility  tests 180,  310 

Fractions • 298 

Fuses,  carrying  capacity 290 

Glass  insulators 95,  96 

Graded  cables ,  60,  83 

Graphical  determination  of  stresses  in  spans 161 

Grounding  of  cables 78,  80 

Hammond,  R.,  on  life  of  cables 238 

Hayden,  J.  L.  R.,  on  electrolysis 243 

Heating  of  conductors,  see  Carrying  capacity. 

Hewlett  insulator 98,  199 

Hunting  of  converters 155 

Hysteresis  test  of  rubber 66 

Impedance 274 

Inductance,  of  circuits 270 

formulae 324 


INDEX  331 

( 

PAGE 

Inductance,  iron  wires 274 

parallel  wires 321 

Insects  attacking  cables 244 

Installation  of  overhead  wires 224 

Installation  of  underground  wires 220 

Insulated  cables  underground 76 

Insulated  negative  feeders 241 

Insulating  sleeves 234 

Insulation,  general 59 

graded 60,  83 

paper 71,  87 

resistance  calculations 296 

resistance  measurements 210,  212 

rubber,  see  Rubber. 

thickness  of 82,  84,  87,  89,  291 

underground 76 

uniform  structure 59 

Insulators 94,  197 

Inverted  three-phase  system 105 

Isolated  section  of  third  rail 251 

Joining  insulated  cables 229 

Jona,  E 294 

Kapp's  modification  of  Kelvin's  law . .   157 

Kelvin's  law 112,  156 

Kennelly  and  Fessenden 30 

Keiley's  (J.  D.)  circuit -breaker  house  system 120 

Kilovolt 133 

Kirschoff's  laws 33 

Lamp  wiring  calculations 107 

Langan,  J 85 

Laying,  definition 13 

Lea  of  hemp 184,  315 

Lead  sheath  thickness 87,  92 


332  INDEX 

PAGE 

Leakage  from  railway  tracks "...  143 

Length  of  spans 1 75 

Length  of  wire  in  span 175 

Levi-Civita,  Prof 294 

Lichenstein,  L 42 

Life  of  cables  in  ducts 238 

Line  capacity,  effects  of 139,  153,  277 

Locating  crosses 215 

Locating  faults 213 

Madison  River  Power  Co 95 

Mains,  calculation  of 107 

Mather,  T. 208 

Matthiessen's  standard 22 

temperature  coefficient 31 

Maxwell's  imaginary  currents 33 

Mechanical  thickness  of  insulation 295 

Megawatt - 133 

Megohms,  calculation  of  . 296 

Megohms,  value  of 317 

Mershon,  R.  D 103 

Messenger  cable,  current  in 145 

Messenger  wire  construction 226 

Missouri  River  Power  Co 94 

Modulus  of  elasticity i,  310 

Moisture  in  cable 229 

Most  economical  distribution  of  copper 117,  299 

Multiplex  cables 91,  92,  182,  312,  318 

Murray  loop  test 213 

Negative  boosters 127 

Networks,  resistance  of 33 

New  York,  New  Haven,  and  Hartford  R.  R.  trolley 142 

Ohms  per  mile,  copper  and. aluminum 137 

Ohms  per  thousand  feet,  copper 25,  26 


INDEX  333 

- 

PAGB 

Ohms,  aluminum 27 

Old  English  wire  gauge 1 1 

Oval  duplex  cables 182,  312 

Overhead  circuits,  inductance 270 

Ozite 196,  236 

Paper  insulation,  dielectric  strength 72 

general 71 

hygroscopic  nature  of 71 

in  cold  weather 88 

installed  vertically 82 

resistance  and  time  of  electrification 73 

specifications 196,  320 

temperature  coefficient  of  resistance 72 

thickness  of 87 

triplex  cables 91 

underground 76 

water  in 72,  76 

Para  rubber 62 

Paraffin  wax 236 

Pender,  H.,  alternating  current  transmission 133,  153,  304,  306 

Kelvin's  law 157 

slide  rule  method  for  temperature  resistance  calculations 32 

wire  spans 159,  308 

Permissible  potential  drop in 

Petticoat  insulators 95 

Pin,  eucalyptus 102 

locust 102 

Long  Island  R.  R 101 

standard  A.  I.  E.  E 102 

Pin  shield  insulators 95 

Pitch,  definition 13 

diameter,  definition 13 

factor,  definition 13 

minimum 17 

standard 16 


334  INDEX 

PAGE 

Polyphase  systems 105 

Porcelain,  absorption 95,  190 

insulators 94 

Potential  drop  and  car  lights in 

Potential,  importance  of  high 104 

Potential  tests,  cambric 90 

Paper 87 

rubber 85,  87 

Power  factor 133,  135 

Power  loss  calculations 133 

Pressure  drop  calculations 107,  in,  133 

Protection  from  electrolysis 240 

Quarter-phase  systems 105,  106 

Racks  for  cables 78 

Rail  bonds 252 

Rail-bond  specifications 196 

Rail  reactance ' 143 

Railway  circuits , in,  245 

Railway  feeders,  underground 76 

Reactance,  circuits 270 

excessive 136 

increment 137 

per  mile  of  No.  oooo  wire 134 

single-phase  trolley 144 

tables 273 

Reeling,  effects  of,  upon  insulation 88 

Resistance,  aluminum  wire 27 

copper 23 

copper  wire 25,  26 

increase  of>  due  to  spiralling 29 

with  infrequent  cross-bonds 119,  302 

Resistance  measurements,  accuracy  of 205 

differential  galvanometer 203 

substitution 204,  210 


INDEX  335 

PAGE 

Resistance  measurements,  voltmeter  and  ammeter 202 

Resistances,  plug  type 205 

Reichsanstalt 207 

standard 205 

Roberts,  E.  P.,  wiring  slide  rule 109 

Root -mean -square •• 126 

Rope  strand,  definition 13 

Rotary  converters  and  line  drop 155 

Rubber 62 

Rubber-covered  wire,  Engineers'  Association  specification, 

86,87,  193,  3i9 

Rubber  insulation,  albumin  in 70 

black  or  white 70 

desirable  qualities 61 

dieletric  strength 71 

effect  of  light  upon 69 

effect  of  high  temperature 67,  68 

equilibrium  of 61 

for  high-tension  service 194 

general 60 

hysteresis  test 66 

insulation  resistance 65,  86,  296 

litharge  in 71 

megohms 65,  86,  296 

over-mastication 69,  31 7 

photo-sensitiveness 69 

potential  tests -  -  -  85,  87 

resinous  matter  in » 67 

set  after  'stretching 64 

specific  resistance 65,  296 

specifications 189,  193,  317 

stretch  test 64,  191,  193,  318 

submarine 81,  91 

sulphur  in 66 

temperature  coefficient  of  resistance 65,  192 

tenacity  and  temperature 68 


336  INDEX 

PAGB 

Rubber  insulation,  tensile  strength 63 

thickness  of 84,  85,  291 

triplex 91 

U.  S.  Navy 63 

under  water 69,  91 

weathering 70 

Russel,  A 280,  321 

Ryan,  H.  J 102 

Sag  in  spans 159,  161,  308 

Schwartz,  A 68 

Self-induction 270,  321 

Sheath,  composition „ 184 

melted  by  current 76 

thickness 87,  92 

Shoddy,  use  of 189 

Short  circuits 77,  79 

Short  circuit  indiactor 93 

Short  period  carrying  capacity 54,  287 

Shunts 207 

Signal  circuits  and  grounding 79 

Single-phase  railway  feeders 142 

Size  of  conductors 104 

Size  of  wire  for  lighting 107 

for  transmission 133 

Skin  effect 40,  284 

Sleeves  for  cable  joints 230,  232 

Sleeves,  settlement  in 188 

Slide  rule  for  wiring  calculations 109 

Solid  system 79 

Soxhlet  extractor 193 

Spans,  calculations  for 159 

equations  of 1 75 

length  of 175 

stresses  in 159,  308 

Specifications  for  bare  cables 179,  310 


INDEX  337 

PAGB 

Specifications  for  insulated  cables 181,  311 

high-tension  insulator 197 

paper  insulation 196,  320 

rail  bonds 196 

rubber  insulation 189,  193,  317,  319 

varnished  cloth 195,  320 

Spiralling,  increase  of  resistance  due  to 29 

Splicing 227,  312 

Splicing  diagram 235 

Square  root  of  mean  square 126 

Static  discharges  in  cables 80,  312 

Steel  taping 185 

Steinmetz,  C.  P 106 

Strand,  see  Cable. 

definition 13 

diameter  of  wires  in 19 

Stranded  conductors,  dielectric  stress  in 294 

Stranding,  definition 13 

Stress  in  dielectric 293 

Stresses  in  spans 159,  161,  308 

Stretch  test  for  rubber 191,  194,  318 

Stubb's  wire  gauge 10,  1 1 

Submarine  cables 81 

Sulphur  in  rubber  insulation 66 

Systems  of  distribution 104 

Tangents  and  cosines 139 

Tape  on  rubber  insulation 314 

Tape,  width  of 83 

Taping 184,  314 

Temperature  coefficient  of  resistance,  cambric 75 

metals 30 

Paper 72 

rubber 65,  192,  318 

Temperature  resistance  calculations 30,  32 

Testing  for  capacity 209 


338  INDEX 

PAGE 

Testing  for  inductance 202 

insulation  resistance 210,  212 

resistance,  see  Resistance. 

Tests  on  insulated  cable 185 

Tests  on  rubber  insulation 190,  317 

Thermit  welding 266 

Three-conductor  cables 91,  92 

Three-phase  systems 105,  106 

Three-wire  system no 

Thickness  of  insulation,  calculation  of 291 

cambric 89,  90 

paper 87 

reasons  for  specifying 314 

rubber 84,  85,  87,  291 

Third  rail  circuits 245 

sectionalizing 246 

Tin  in  sheathing 315 

Tinning  copper 231 

Transmission  calculations,  alternating  currents 133 

basis  of 304,  306 

direct  current  lighting 107 

direct  current  railways in 

exact  method  with  capacity  and  leakage 153,  306 

Triplex  cable,  belted  and  unbelted 91 

diameter 92 

Trolley  calculations,  alternating  current 142 

Underground  cables 76 

Universal  shunt 208 

Uplift  on  poles 1 70,  1 76 

Value  of  cable  after  installation 238 

Varley  loop  test 215 

Varnished  cloth  or  cambric,  effect  of  oil  upon  . 74 

flexibility 74 

general 73 


INDEX  339 

•  * 

PAGE 

Varnished  cloth  or  cambric  in  sunlight 82 

subjected  to  vibration 74 

temperature  coefficient 75 

thickness 89,  90 

Vertical  stresses  on  poles 170,  176 

Volatile  matter  in  rubber 317 

Voltage  drop  equations 125 

Voltage  drop  and  synchronous  apparatus 155 

Voltages  for  transmission 104,  107 

Voltax 196,  236 

Volume  unit,  circular-mil-foot 1 16 

Washburn  and  Moen  gauge 1 1 

Water,  cables  under 81 

Watts  lost,  equations  of 118,  125 

Weber,  C.  O 67,  69,  70,  71,  193 

Welded  rail  joints 265,  266,  268 

Welding,  Thermit  process 266 

Wheatstone's  bridge 200 

Winch  for  cable  drawing 221 

Wind  velocity '. 165 

Wiping  sleeve  joint 234 

Wire,  calculation  of  tables 282 

gauges ii 

resistance,  ohms  per  1000  feet 25,  26,  27 

resistance,  ohms  per  mile 137 

size  for  lighting 107 

spans,  stresses  in 159 

Wiring  of  ducts 187,  220 


LIST  OF  WORKS 


ON 


ELECTRICAL    SCIENCE 

PUBLISHED  AND  FOR   SALE   BY 

D.    VAN   NOSTRAND  COMPANY, 

23  Murray  and  27  Warren  Streets,  New  York. 


ABBOTT,  A.  V.  The  Electrical  Transmission  of  Energy.  A  Manual  for 
the  Design  of  Electrical  Circuits.  Fifth  Edition,  enlarged  and  rewritten. 
With  many  Diagrams,  Engravings  and  Folding  Plates.  8vo.,  cloth, 
675  pp Net,  $5.00 

ADDYMAN,  F.  T.  Practical  X-Ray  Work.  Illustrated.  8vo.,  cloth,  200 
pp Net,  $4.00 

ALEXANDER,  J.  H.  Elementary  Electrical  Engineering  in  Theory  and 
Practice.  A  class-book  for  junior  and  senior  students  and  working 
electricians.  Illustrated.  12mo.,  cloth,  208  pp $2.0(? 

ANDERSON,  GEO.  L.,  A.M.  (Capt.  U.S.A.).  Handbook  for  the  Use  o\ 
Electricians  in  the  operation  and  care  of  Electrical  Machinery  and 
Apparatus  of  the  United  States  Seacoast  Defenses.  Prepared  under 
the  direction  of  Lieut.-General  Commanding  the  Army.  Illustrated. 
8vo.,  cloth,  161  pp $3.00 

ARNOLD,  E.  Armature  Windings  of  Direct-Current  Dynamos.  Exten- 
3ion  and  Application  of  a  general  Winding  Rule.  Translated  from 
the  original  German  by  Francis  B.  DeCress.  Illustrated.  8vo., 
cloth,  124  pp $2.00 


ASHE,  S.  W.,  and  KEILEY,  J.  D.  Electric  Railways  Theoretically  and 
Practically  Treated.  Illustrated.  12mo.,  cloth. 

Vol.  I.     Rolling  Stock.     Second  Edition.     285  pp Net,  $2 . 50 

Vol.  II.     Substations  and  Distributing  Systems.     296  pp .  . .  .  Net,  $2 . 50 

ATKINSON,  A.  A.,  Prof.  (Ohio  Univ.).  Electrical  and  Magnetic  Calcula- 
tions. For  the  use  of  Electrical  Engineers  and  others  interested  in 
the  Theory  and  Application  of  Electricity  and  Magnetism.  Third 
Edition,  revised.  Illustrated.  8vo.,  cloth,  310  pp Net,  $1 . 50 

PHILIP.  The  Elements  of  Dynamic  Electricity  and  Magnetism. 

Fourth  Edition.  Illustrated.  12mo.,  cloth,  405  pp $2.00 

Elements  of  Electric  Lighting,  including  Electric  Generation,  Measure- 
ment, Storage,  and  Distribution.  Tenth  Edition,  fully  revised  and  new 

matter  added.  Illustrated.  12mo.,  cloth,  280  pp $1 .50 

Power  Transmitted  by  Electricity  and  Applied  by  the  Electric  Motor, 
including  Electric  Railway  Construction.  Illustrated.  Fourth  Edition, 
fully  revised  and  new  matter  added.  12mo.,  cloth,  241  pp.  . .$2.00 

AYRTON,  HERTHA.  The  Electric  Arc.  Illustrated.  8vo.,  cloth,  479 
pp Net,  $5.00 

W.  E.  Practical  Electricity.  A  Laboratory  and  Lecture  Course. 

Illustrated.  12mo.,  cloth,  643  pp $2 .00 

BIGGS,  C.  H.  W.  First  Principles  of  Electricity  and  Magnetism.  Illus- 
trated. 12mo.,  cloth,  '495  pp $2 .00 

BONNEY,  G.  E.  The  Electro-Plater's  Hand  Book.  A  Manual  for  Ama- 
teurs and  Young  Students  of  Electro-Metallurgy.  Fourth  Edition, 
enlarged.  61  Illustrations.  12mo.,  cloth,  208  pp $1 .20 

BOTTONE,  S.  R.  Magnetos  For  Automobilists ;  How  Made  and  How  Used. 
A  handbook  of  practical  instruction  on  the  manufacture  and  adapta- 
tion of  the  magneto  to  the  needs  of  the  motorist.  Illustrated.  12mo., 

cloth,  88  pp Net,  $1 .00 

Electric  Bells  and  All  about  Them.  12mo.,  cloth 50  cents 

Electrical  Instrument-Making  for  Amateurs.  A  Practical  Handbook. 
Enlarged  by  a  chapter  on  "  The  Telephone."  Sixth  Edition.  With 

48  Illustrations.  12mo.,  cloth 50  cents 

Electric  Motors,  How  Made  and  How  Used.  Illustrated.  12mo.,  cloth, 
168  pp 75  cents 

BOWKER,  WM.  R.  Dynamo,  Motor,  and  Switchboard  Circuits  for  Elec- 
trical Engineers:  a  practical  book  dealing  with  the  subject  ot  direct, 
alternating,  and  polyphase  currents.  Second  Edition.  130  Illustra- 
tions. 8vo.,  cloth,  180  pp Net,  $2 . 50 


BUBIER,  E.  T.  Questions  and  Answers  about  Electricity.  A  First  Book 
for  Beginners.  12mo.,  cloth 50  cents 

CARTER,  E.  T.  Motive  Power  and  Gearing  for  Electrical  Machinery;  a 
treatise  on  the  theory  and  practice  of  the  mechanical  equipment  of 
power  stations  for  electric  supply  and  for  electric  traction.  Second 
Edition,  revised.  Illustrated.  8vo.,  cloth,  700  pp Net,  $5.00 

CHILD,  CHAS.  T.  The  How  and  Why  of  Electricity:  a  book  of  informa- 
tion for  non-technical  readers,  treating  of  the  properties  of  Elec- 
tricity, and  how  it  is  generated,  handled,  controlled,  measured,  and 
set  to  work.  Also  explaining  the  operation  of  Electrical  Apparatus. 
Illustrated.  8vo.,  cloth,  140  pp $1  .00 

CLARK,  D.  K.  Tramways,  Their  Construction  and  Working.  Second 
Edition.  Illustrated.  8vo.,  cloth,  758  pp $9.00 

COOPER,  W.  R.     Primary  Batteries:    their  Theory,  Construction,  and  Use. 

131  Illustrations.     8vo.,  cloth,  324  pp Net,  $4.00 

The  Electrician  Primers.  Being  a  series  of  helpful  primers  on  electrical 
subjects,  for  use  of  students,  artisans,  and  general  readers.  Second 
Edition.  Illustrated.  Three  volumes  in  one.  8vo.,  cloth .  .  Net,  $5 . 00 

Vol.  I.— Theory Net,  $2 .00 

Vol.  II.— Electric  Traction,  Lighting  and  Power Net,  $3 .00 

Vol.  m.— Telegraphy,  Telephony,  etc Net,  $2  00 

CROCKER,  F.  B.  Electric  Lighting.  A  Practical  Exposition  of  the  Art 
for  the  use  of  Electricians,  Students,  and  others  interested  in  the 
Installation  or  Operation  of  Electric-Lighting  Plants. 

Vol.  I. — The  Generating  Plant.  Seventh  Edition,  entirely  revised.  Illus- 
trated. 8vo.,  cloth,  482  pp $3 .00 

Vol.  II. — Distributing  System  and  Lamps.  Sixth  Edition.  Illustrated. 
8vo.,  cloth,  505  pp $3 .00 

and   ARENDT,    M.     Electric    Motors :    Their   Action,    Control,    and 

Application.     Illustrated.     8vo.,  cloth In  Press 

- and  WHEELER,  S.  S.     The  Management  of  Electrical  Machinery. 

Being  a  thoroughly  revised  and  rewritten  edition  of  the  authors'  "Prac- 
tical Management  of  Dynamos  and  Motors."  Seventh  Edition. 
Illustrated.  IGmo.,  cloth,  232  pp Net,  $1 .00 

CUSHING,  H.  C.,  Jr.  Standard  Wiring  for  Electric  Light  and  Power. 
Illustrated.  16mo.,  leather,  156  pp $1 .00 

DAVIES,  F.  H.  Electric  Power  and  Traction.  Illustrated.  8vo.,  cloth, 
293  pp.  (Van  Nostrand's  Westminster  Series.) Net,  $2.00 


DIBDIN,W.J.  Public  Lighting  by  Gas  and  Electricity.  With  many  Tables, 
Figures,  and  Diagrams.  Illustrated.  8vov  cloth,  537  pp. Net,  $8.00 

DINGER,  Lieut.  H.  C.  Handbook  for  the  Care  and  Operation  of  Naval 
Machinery.  Second  Edition.  124  Illustrations.  16mo.,  cloth, 
302  pp Net,  $2.00 

DYNAMIC  ELECTRICITY:  Its  Modern  Use  and  Measurement,  chiefly 
in  its  application  to  Electric  Lighting  and  Telegraphy,  including: 
1.  Some  Points  in  Electric  Lighting,  by  Dr.  John  Hopkinson.  2.  On 
the  Treatment  of  Electricity  for  Commercial  Purposes,  by  J.  N.  Shool- 
biad.  3.  Electric-Light  Arithmetic,  by  R.  E.  Day,  M.E.  Fourth 
Edition.  Illustrated.  16mo.,  boards,  166  pp.  (No.  71  Van  Nos- 
trand's  Science  Series.) 50  cents 

EDGCUMBE,  K.  Industrial  Electrical  Measuring  Instruments.  Illus- 
trated. 8vo.,  cloth,  227  pp Net,  $2 .50 

ERSKINE-MURRAY,  J.  A  Handbook  of  Wireless  Telegraphy :  Its  Theory 
and  Practice.  For  the  use  of  electrical  engineers,  students,  and 
operators.  Illustrated.  8vo.,  cloth,  320  pp Net,  $3 .50 

EWING,  J.  A.  Magnetic  Induction  in  Iron  and  other  Metals.  Third 
Edition,  revised.  Illustrated.  8vo.,  cloth,  393  pp Net,  $4.00 

FISHER,  H.  K.  C.,  and  DARBY,  W.  C.  Students'  Guide  to  Submarine  Cable 
Testing.  Third  Edition,  new,  enlarged.  Illustrated.  8vo.,  cloth, 
326  pp Net,  $3.50 

FLEMING,  J.  A.,  Prof.  The  Alternate-Current  Transformer  in  Theory 
and  Practice. 

Vol.  I.:  The  Induction  of  Electric  Currents.  Fifth  Issue.  Illustrated. 
8vo.,  cloth,  641  pp Net,  $5.00 

Vol.  II. :  The  Utilization  of  Induced  Currents.  Third  Issue.  Illus- 
trated. 8vo.,  cloth,  587  pp Net,  $5 .00 

Handbook  for  the  Electrical  Laboratory  and  Testing  Room.  Two  Vol- 
umes. Illustrated.  8vo.,  cloth,  1160  pp.  Each  vol Net,  $5 . 00 

FOSTER,  H.  A.  With  the  Collaboration  of  Eminent  Specialists.  Electri- 
cal Engineers'  Pocket  Book.  A  handbook  of  useful  data  for  Elec- 
tricians and  Electrical  Engineers.  With  innumerable  Tables,  Dia- 
grams, and  Figures.  The  most  complete  book  of  its  kind  ever  pub- 
lished, treating  of  the  latest  and  best  Practice  in  Electrical  Engineer- 
ing. Fifth  Edition,  completely  revised  and  enlarged.  Fully  Illustrated. 
Pocket  Size.  Leather.  Thumb  Indexed.  1636  pp $5.00 


GANT,  L.  W.  Elements  of  Electric  Traction  for  Motormen  and  Others. 
Illustrated  with  diagrams.  Svo.,  cloth,  217  pp Net,  $2.50 

GERHARDI,  C.  H.  W.  Electricity  Meters;  their  Construction  and  Man- 
agement. A  practical  manual  for  engineers  and  students.  Illus- 
trated. 8vo.,  cloth,  337  pp Net,  $4 .00 

GORE,  GEORGE.  The  Art  of  Electrolytic  Separation  of  Metals  (Theoret- 
ical and  Practical).  Illustrated.  8vo.,  cloth,  295  pp Net,  $3 . 50 

GRAY,  J.  Electrical  Influence  Machines:  Their  Historical  Development 
and  Modern  Forms.  With  Instructions  for  making  them.  Second 
I'ldition,  revised  and  enlarged.  With  105  Figures  and  Diagrams. 
12mo.,  cloth,  296  pp $2.00 

HAMMER,  W.  J.  Radium,  and  Other  Radio  Active  Substances;  Polo- 
nium, Actinium,  and  Thorium.  With  a  consideration  of  Phospho- 
rescent and  Fluorescent  Substances,  the  properties  and  applications 
of  Selenium,  and  the  treatment  of  disease  by  the  Ultra-Violet  Light. 
With  Engravings  and  Plates.  Svo.,  cloth,  72  pp $1 .00 

HARRISON,  N.  Electric  Wiring  Diagrams  and  Switchboards.  Illus- 
trated. 12mo.,  cloth,  272  pp $1 .50 

HASKINS,  C.  H.  The  Galvanometer  and  its  Uses.  A  Manual  for  Elec- 
tricians and  Students.  Fifth  Edition,  revised.  Illustrated.  16mo., 
morocco,  75  pp $1 . 50 

HAWKINS,  C.  C.,  and  WALLIS,  F.  The  Dynamo:  Its  Theory,  Design, 
and  Manufacture.  Fourth  Edition,  revised  and  enlarged.  1 90  Illustra- 
tions. Svo.,  cloth,  925  pp $3.00 

HAY,  ALFRED.    Principles  of  Alternate-Current  Working.    Second  Edition. 

Illustrated.     12mo.,  cloth,  390  pp $2.00 

Alternating    Currents;    their    theory,    generation,    and    transformation. 
Second  Edition.     191  Illustrations.     8vo.,  cloth,  319pp.  .  .Net,  $2.50 
An    Introductory    Course    of    Continuous-Current    Engineering.     Illus- 
trated.    Svo.,  cloth,  327  pp Net,  $2 .50 

HEAVISIDE,  0.  Electromagnetic  Theory.  Two  Volumes  with  Many 
Diagrams.  Svo.,  cloth,  1006  pp.  Each  Vol Net,  $5.00 

HEDGES,  K.  Modern  Lightning  Conductors.  An  illustrated  Supple- 
ment to  the  Report  of  the  Research  Committee  of  1905,  with  notes 
as  to  methods  of  protection  and  specifications.  Illustrated.  Svo. 
cloth,  119  pp Net,  $3.00 


HOBART,  H.  M.  Heavy  Electrical  Engineering.  Illustrated.  8vo., 
cloth,  307pp.. ." Net,  $4.50 

HOBBS,  W.  R.  P.  The  Arithmetic  of  Electrical  Measurements.  With 
numerous  examples,  fully  worked.  Twelfth  Edition.  12mo.,  cloth, 
126  pp 50  .  cents 

HOMANS,J.E.  A  B  C  of  the  Telephone.  With  269  Illustrations.  12mo., 
cloth,  352  pp $1  .00 

HOPKINS,  N.  M.  Experimental  Electrochemistry,  Theoretically  and  Prac- 
tically Treated.  Profusely  illustrated  with  130  new  drawings,  diagrams, 
and  photographs,  accompanied  by  a  Bibliography.  Illustrated. 
8vo.,  cloth,  29S  pp Net,  $3 .00 

HOUSTON,  EDWIN  J.  A  Dictionary  of  Electrical  Words,  Terms,  and 
Phrases.  Fourth  Edition,  rewritten  and  greatly  enlarged.  582  Illus- 
trations. 4to.,  cloth Net,  $7.00 

'A  Pocket  Dictionary  of  Electrical  Words,  Terms,  and  Phrases.      12mo., 
cloth,  950  pp Net,  $2.50 

HUTCHINSON,  R.  W.,  Jr.  Long-Distance  Electric  Power  Transmission: 
Being  a  Treatise  on  the  Hydro-Electric  Generation  of  Energy;  Its 
Transformation,  Transmission,  and  Distribution.  Second  Edition. 
Illustrated.  12mo.,  cloth,  350  pp Net,  $3 .00 

and  IHLSENG,  M.  C.     Electricity  in  Mining.     Being  a  theoretical 

and  practical  treatise  on  the  construction,  operation,  and  mainte- 
nance of  electrical  mining  machinery.     12mo.,  cloth In  Press 

INCANDESCENT  ELECTRIC  LIGHTING.  A  Practical  Description  of 
the  Edison  System,  by  H.  Latimer.  To  which  is  added:  The  Design 
and  Operation  of  Incandescent  Stations,  by  C.  J.  Field;  A  Descrip- 
tion of  the  Edison  Electrolyte  Meter,  by  A.  E.  Kennelly;  and  a 
Paper  on  the  Maximum  Efficiency  of  Incandescent  Lamps,  by  T.  W. 
Howell.  Fifth  Edition.  Illustrated.  16mo.,  cloth,  140  pp.  (No. 
57  Van  Nostrand's  Science  Series.) 50  cents 

INDUCTION  COILS:  How  Made  and  How  Used.  Eleventh  Edition. 
Illustrated.  16mo.,  cloth,  123  pp.  (No.  53  Van  Nostrand's  Science 
Series.) 50  cents 

JEHL,  FRANCIS,  Member  A.I.E.E.  The  Manufacture  of  Carbons  for 
Electric  Lighting  and  other  purposes.  Illustrated  with  numerous 
Diagrams,  Tables,  and  Folding  Plates.  8vo.,  cloth.  232  pp .  .  Net,  $4 . 00 


JONES,  HARRY  C.  The  Electrical  Nature  of  Matter  and  Radioactivity. 
12mo.,  cloth,  212  pp. $2.00 

KAPP,  GISBERT.  Electric  Transmission  of  Energy  and  its  Transforma- 
tion, Subdivision,  and  Distribution.  A  Practical  Handbook.  Fourth 
Edition,  thoroughly  revised.  Illustrated .  12mo.,  cloth,  445  pp .  .  $3 . 50 

Alternate-Current  Machinery.  Illustrated.  16mo.,  cloth,  190pp.  (No. 
96  Van  Nostrand's  Science  Series.) 50  cents 

Dynamos,  Alternators  and  Transformers.  Illustrated.  8vo.,  cloth,  507 
PP $4.00 

KELSEY,  W.  R.  Continuous-Current  Dynamos  and  Motors,  and  their 
Control;  being  a  series  of  articles  reprinted  from  the  "Practical 
Engineer,"  and  completed  by  W.  R.  Kelsey,  B.Sc.  With  Tables, 
Figures,  and  Diagrams.  8vo.,  cloth,  439  pp $2 . 50 

KEMPE,  H.  R.  A  Handbook  of  Electrical  Testing.  Seventh  Edition, 
revised  and  enlarged.  Illustrated.  8vo.,  cloth,  706  pp. . .  Net,  $6.00 

KENNEDY,   R.     Modern   Engines   and   Power   Generators.     Illustrated. 

8vo.,  cloth,  5  vols.     Each $3 . 50 

Electrical  Installations  of  Electric  Light,  Power,  and  Traction  Machinery. 
Illustrated.  8vo.,  cloth,  5  vols.  Each $3 . 50 

KENNELLY,  A.  E.  Theoretical  Elements  of  Electro-Dynamic  Machinery. 
Vol.  I.  Illustrated.  8vo.,  cloth,  90  pp $1 . 50 

KERSHAW,  J.  B.  C.     The  Electric  Furnace  in  Iron  and  Steel  Production. 

Illustrated.     8vo.,  cloth,  74  pp Net,  $1 . 50 

Electrometallurgy.  Illustrated.  8vo.,  cloth,  303  pp.  (Van  Nos- 
trand's Westminster  Series.) Net.  $2 .00 

KINZBRUNNER,  C.     Continuous-Current  Armatures ;    their  Winding  and 

Construction.     79  Illustrations.     8vo.,  cloth,  80  pp Net,  $1 .50 

Alternate-Current  Windings ;  their  Theory  and  Construction.  89  Illus- 
trations. 8vo.,  cloth,  80  pp Net,  $1  . 50 

KOESTER,  FRANK.  Steam-Electric  Power  Plants.  A  practical  treatise 
on  the  design  of  central  light  and  power  stations  and  their  econom- 
ical construction  and  operation.  Fully  Illustrated.  4to.,  cloth, 
455  pp Net,  $5.00 

LARNER,  E.  T.  The  Principles  of  Alternating  Currents  for  Students  of 
Electrical  Engineering.  Illustrated  with  Diagrams.  12mo.,  cloth, 
144  pp Net,  $1 .25 


LEMSTROM,  S.  Electricity  in  Agriculture  and  Horticulture.  Illustrated. 
8vo.,  cloth Net,  $1  .50 

LIVERMORE,  V.  P.,  and  WILLIAMS,  J.  How  to  Become  a  Competent 
Motonnan :  Being  a  practical  treatise  on  the  proper  method  of  oper- 
ating a  street-railway  motor-car;  also  giving  details  how  to  over- 
come certain  defects.  Second  Edition.  Illustrated.  16mo.,  cloth, 
247  pp Net,  $1 .00 

LOCKWOOD,  T.  D.  Electricity,  Magnetism,  and  Electro-Telegraphy.  A 
Practical  Guide  and  Handbook  of  General  Information  for  Electri- 
cal Students,  Operators,  and  Inspectors.  Fourth  Edition.  Illus- 
trated. 8vo.,  cloth,  374  pp $2.50 

LODGE,  OLIVER  J.  Signalling  Across  Space  Without  Wires:  Being  a 
description  of  the  work  of  Hertz  and  his  successors.  Third  Edition. 
Illustrated.  8vo.,  cloth Net,  $2 .00 

LORING,  A.  E.  A  Handbook  of  the  Electro-Magnetic  Telegraph. 
Fourth  Edition,  revised.  Illustrated.  16mov  cloth,  116  pp.  (No. 
39  Van  Nostrand's  Science  Series.) 50  cents 

LUPTON,  A.,  PARR,  G.  D.  A.,  and  PERKIN,  H.     Electricity  Applied  to 

Mining.     Second    Edition.     With    Tables,    Diagrams,    and    Folding 
Plates.     8vo.,  cloth,  320  pp Net,  $4.50 

MAILLOUX,  C.  O.  Electric  Traction  Machinery.  Illustrated.  8vo., 
cloth In  Press 

MANSFIELD,  A.  N.  Electromagnets:  Their  Design  and  Construction. 
Second  Edition.  Illustrated.  16mo.,  cloth,  155  pp.  (No.  64.  Van 
Nostrand's  Science  Series.) 50  cents 

MASSIE,  W.  W.,  and  UNDERBILL,  C.  R.  Wireless  Telegraphy  and 
Telephony  Popularly  Explained.  With  a  chapter  by  Nikola  Tesla. 
Illustrated.  12mo.,  cloth,  82  pp Net,  $1 . 00 

MAURICE,  W.  Electrical  Blasting  Apparatus  and  Explosives,  with 
special  reference  to  colliery  practice.  Illustrated.  8vo.,  cloth, 
167  pp Net,  $3.50 

MAVER,  WM.,  Jr.  American  Telegraphy  and  Encyclopedia  of  the  Tele- 
graph Systems,  Apparatus,  Operations.  Fifth  Edition,  revised  and 
enlarged.  490  Illustrations.  8vo.,  cloth,  668  pp Net,  $5 . 00 


MONCKTON,  C.  C.  F.  Radio  Telegraphy.  173  Illustrations.  8vo., 
cloth,  272  pp.  (Van  Nostrand's  Westminster  Series.) Net,  $2.00 

MUNRO,  J.,  and  JAMIESON,  A.  A  Pocket-Book  of  Electrical  Rules  and 
Tables  for  the  Use  of  Electricians,  Engineers,  and  Electrometallurgists. 
Eighteenth  Revised  Edition.  32mo.,  leather,  735  pp $2.50 

NIPHEP.  FRANCIS  E.  Theory  of  Magnetic  Measurements.  With  an 
Appendix  on  the  Method  of  Least  Squares.  Illustrated.  12mo., 
cloth,  94  pp $1 .00 

NOLL,  AUGUSTUS.  How  to  Wire  Buildings.  A  Manual  of  the  Art  of 
Interior  Wiring.  Fourth  Edition.  Illustrated.  12mo.,  cloth, 
165  pp $1 .50 

OHM,  G.  S.  The  Galvanic  Circuit  Investigated  Mathematically.  Berlin, 
1827.  Translated  by  William  Francis.  With  Preface  and  Notes 
by  Thos.  D.  Lockwood.  Second  Edition.  Illustrated.  16mo.,  cloth, 
269  pp.  (No.  102  Van  Nostrand's  Science  Series.) 50  cents 

OUDIN,  MAURICE  A.  Standard  Polyphase  Apparatus  and  Systems. 
Fifth  Edition,  revised.  Illustrated  with  many  Photo-reproductions, 
Diagrams,  and  Tables.  8vo.,  cloth,  369  pp Net,  $3 . 00 

PALAZ,  A.  Treatise  on  Industrial  Photometry.  Specially  applied  to 
Electric  Lighting.  Translated  from  the  French  by  G.  W.  Patterson, 
Jr.,  and  M.  R.  Patterson.  Second  Edition.  Fully  Illustrated. 
8vo.,  cloth,  324  pp $4.00 

PARR,  G.  D.  A.  Electrical  Engineering  Measuring  Instruments  for  Com- 
mercial and  Laboratory  Purposes.  With  370  Diagrams  and  Engrav- 
ings. 8vo.,  cloth,  328  pp Net,  $3.50 

PARSHALL,  H.  F.,  and  HOBART,  H.  M.  Armature  Windings  of  Electric 
Machines.  Third  Edition.  With  140  full-page  Plates,  65  Tables, 
and  165  pages  of  descriptive  letter-press.  4to.,  cloth,  300  pp.  .$7.50 

Electric  Railway  Engineering.  With  437  Figures  and  Diagrams 
and  many  Tables.  4to.,  cloth,  475  pp Net,  $10.00 

Electric  Machine  Design.  Being  a  revised  and  enlarged  edition  of 
"Electric  Generators."  648  Illustrations.  4to.,  half  morocco,  601 
pp Net,  $12.50 


PERRINE,  F.  A.  C.  Conductors  for  Electrical  Distribution :  Their  Manu- 
facture and  Materials,  the  Calculation  of  Circuits,  Pole-Line  Construc- 
tion, Underground  Working,  and  other  Uses.  Second  Edition.  Illus- 
trated. 8vo.,  cloth,  287  pp Net,  $3 .50 

POOLE,  C.  P.  The  Wiring  Handbook  with  Complete  Labor-saving  Tables 
and  Digest  of  Underwriters'  Rules.  Illustrated.  12mo.,  leather, 
85  pp Net,  $1 .00 

POPE,  F.  L.  Modem  Practice  of  the  Electric  Telegraph.  A  Handbook 
for  Electricians  and  Operators.  Seventeenth  Edition.  Illustrated. 
8vo.,  cloth,  234  pp $1 .50 

RAPHAEL,  F.  C.  Localization  of  Faults  in  Electric  Light  Mains.  Second 
Edition,  revised.  Illustrated.  Svo.,  cloth,  205  pp Net,  $3.00 

RAYMOND,  E.  B.  Alternating-Current  Engineering,  Practically  Treated. 
Third  Edition,  revised.  With  many  Figures  and  Diagrams.  8vo., 
cloth,  244  pp Net,  $2.50 

RICHARDSON,  S.  S.  Magnetism  and  Electricity  and  the  Principles  of  Elec- 
trical Measurement.  Illustrated.  12mo.,  cloth,  596  pp .  .  Net,  $2 . 00 

ROBERTS,  J.  Laboratory  W6rk  in  Electrical  Engineering — Preliminary 
Grade.  A  series  of  laboratory  experiments  for  first-  and  second-year 
students  in  electrical  engineering.  Illustrated  with  many  Diagrams. 
8vo.,  cloth,  218  pp Net,  $2 .00 

ROLLINS,  W.  Notes  on  X-Light.  Printed  on  deckle  edge  Japan  paper. 
400  pp.  of  text,  152  full-page  plates.  8vo.,  cloth Net,  $7.50 

RUHMER,  ERNST.  Wireless  Telephony  in  Theory  and  Practice.  Trans- 
lated from  the  German  by  James  Erskine-Murray.  Illustrated. 
8vo.,  cloth,  224  pp Net,  $3.50 

RUSSELL,  A.  The  Theory  of  Electric  Cables  and  Networks.  71  Illus- 
trations. 8vo.,  cloth,  275  pp Net,  $3.00 

SALOMONS,  DAVID.     Electric-Light  Installations.     A  Practical  Hand- 
book.    Illustrated.     12mo.,  cloth. 
Vol.1.:    Management  of  Accumulators.     Ninth  Edition.     178  pp.  $2. 50 

Vol.  II.:    Apparatus.     Seventh  Edition.     318  pp $2.25 

Vol.  III. :    Application.     Seventh  Edition.     234  pp $1 . 50 


SCHELLEN,  H.  Magneto-Electric  and  Dynamo-Electric  Machines.  Their 
Construction  and  Practical  Application  to  Electric  Lighting  and  the 
Transmission  of  Power.  Translated  from  the  Third  German  Edition 
by  N.  S.  Keith  and  Percy  Neymann.  With  Additions  and  Notes 
relating  to  American  Machines,  by  N.  S.  Keith.  Vol.  I.  With 
353  Illustrations.  Third  Edition.  8vo.,  cloth,  518  pp $5.00 

SEVER,  G.  F.  Electrical  Engineering  Experiments  and  Tests  on  Direct- 
Current  Machinery.  Second  Edition,  enlarged.  With  Diagrams  and 
Figures.  8vo.,  pamphlet,  75  pp Net,  $1 .00 

—  and  TOWNSEND,  F.  Laboratory  and  Factory  Tests  in  Electrical 
Engineering.  Second  Edition,  revised  and  enlarged.  Illustrated.  8vo., 
cloth,  269  pp Net,  $2.50 

SEWALL,  C.  H.  Wireless  Telegraphy.  With  Diagrams  and  Figures. 
Second  Edition,  corrected.  Illustrated .  8vo.,  cloth,  229  pp .  .  Net,  $2 . 00 

Lessons  in  Telegraphy.     Illustrated.     12mo.,  cloth,  104  pp.  .Net,  $1 .00 

T.     Elements    of    Electrical    Engineering.     Third  Edition,    revised. 

Illustrated.     8vo.,  cloth,  444  pp $3 .00 

The  Construction  of  Dynamos  (Alternating  and  Direct  Current).  A 
Text-book  for  students,  engineering  contractors,  and  electricians-in- 
charge.  Illustrated.  8vo.,  cloth,  316  pp $3 .00 

SHAW,  P.  E.  A  First-Year  Course  of  Practical  Magnetism  and  Electricity. 
Specially  adapted  to  the  wants  of  technical  students.  Illustrated. 
8vo.,  cloth,  66  pp.  interleaved  for  note  taking Net,  $1 .00 

SHELDON,  S.,  and  MASON,  H.  Dynamo-Electric  Machinery:  Its  Con- 
struction, Design,  and  Operation. 

Vol.  I.:  Direct-Current  Machines.  Seventh  Edition,  revised.  Illus- 
trated. 8vo.,  cloth,  281  pp Net,  $2.50 

. and  HAUSMANN,  E.  Alternating-Current  Machines :  Being  the  sec- 
ond volume  of  "Dynamo-Electric  Machinery;  its  Construction, 
Design,  and  Operation."  With  many  Diagrams  and  Figures.  (Bind- 
ing uniform  with  Volume  I.)  Seventh  Edition,  rewritten.  8vo., 
cloth,  353  pp Net,  $2 . 50 

SLOANE,  T.  0 'CONOR.  Standard  Electrical  Dictionary.  300  Illustra- 
tions. 12rao.,  cloth,  682  pp $3 . 00 

Elementary  Electrical  Calculations.  How  Made  and  Applied.  Illus- 
trated. 8vo.,  cloth,  300  pp In  Press 


SNELL,  ALBION  T.  Electric  Motive  Power.  The  Transmission  and  Dis- 
tribution of  Electric  Power  by  Continuous  and  Alternating  Currents. 
With  a  Section  on  the  Applications  of  Electricity  to  Milling  Work. 
Second  Edition.  Illustrated.  8vo.,  cloth,  411  pp Net,  $4.00 

SODDY,  F.  Radio-Activity ;  an  Elementary  Treatise  from  the  Stand- 
point of  the  Disintegration  Theory.  Fully  Illustrated.  8vo.,  cloth, 
214  pp Net,  $3.00 

SOLOMON,  MAURICE.  Electric  Lamps.  Illustrated.  8vo.,  cloth.  (Van 
Nostrand's  Westminster  Series.) Net,  $2.00 

STEWART,  A.  Modern  Polyphase  Machinery.  Illustrated.  12mo., 
cloth,  296  pp Net,  $2.00 

SWINBURNE,  JAS.,  and  WORDINGHAM,  C.  H.  The  Measurement  of 
Electric  Currents.  Electrical  Measuring  Instruments.  Meters  for 
Electrical  Energy.  Edited,  with  Preface,  by  T.  Commerford  Martin. 
Folding  Plate  and  Numerous  Illustrations.  16mo,,  cloth,  241  pp. 
(No.  109  Van  Nostrand's  Science  Series.) 50  cents 

SWOOPE,  C.  WALTON.  Lessons  in  Practical  Electricity:  Principles, 
Experiments,  and  Arithmetical  Problems.  An  Elementary  Text- 
book. With  numerous  Tables,  Formulae,  and  two  large  Instruction 
Plates.  Tenth  Edition.  Illustrated.  12mo.,  cloth,  507  pp .  Net,  $2 . 00 

THOM,  C.,  and  JONES,  W.  H.  Telegraphic  Connections,  embracing  recent 
methods  in  Quadruplex  Telegraphy.  20  Colored  Plates.  8vo., 
cloth,  59  pp $1 .50 

THOMPSON,  S.  P.,  Prof.  Dynamo-Electric  Machinery.  With  an  Intro- 
duction and  Notes  by  Frank  L.  Pope  and  H.  R.  Butler.  Fully  Illus- 
trated. 16mo.,  cloth,  214  pp.  (No.  66  Van  Nostrand's  Science 
Series.) 7 50  cents 

Recent  Progress  in  Dynamo-Electric  Machines.  Being  a  Supplement  to 
"Dynamo-Electric  Machinery."  Illustrated.  16mo.,  cloth,  113  pp. 
(No.  75  Van  Nostrand's  Science  Series.).  . . 50  cents 

TOWNSEND,  FITZHUGH.  Alternating  Current  Engineering.  Illus- 
trated. 8vo.,  paper,  32  pp Net,  75  cents 

UNDERBILL,  C.  R.  The  Electromagnet:  Being  a  new  and  revised  edi- 
tion of  "The  Electromagnet,"  by  Townsend  Walcott,  A.  E.  Kennelly, 
and  Richard  Varley.  With  Tables  and  Numerous  Figures  and  Dia- 
grams. 12mo  ,  cloth New  Revised  Edition  in  Press 


URQUHART,  J.  W.  Dynamo  Construction.  A  Practical  Handbook  for 
the  use  of  Engineer  Constructors  and  Electricians  in  Charge.  Illus- 
trated. 12mo.,  cloth $3.00 

Electric  Ship-Lighting.  A  Handbook  on  the  Practical  Fitting  and  Run- 
ning of  Ship's  Electrical  Plant,  for  the  use  of  Ship  Owners  and  Build- 
ers, Marine  Electricians,  and  Sea-going  Engineers  in  Charge.  88 
Illustrations.  12mo.,  cloth,  308  pp $3 .00 

Electric-Light  Fitting.  A  Handbook  for  Working  Electrical  Engineers, 
embodying  Practical  Notes  on  Installation  Management.  Second 
Edition,  with  additional  chapters.  With  numerous  Illustrations. 
12mo.,  cloth $2.00 

Electroplating.  A  Practical  Handbook.  Fifth  Edition.  Illustrated. 
12mo.,  cloth,  230  pp $2 .00 

Electrotyping.     Illustrated.     12mo.,  cloth,  228  pp $2 .00 

WADE,  E.  J.  Secondary  Batteries:  Their  Theory,  Construction,  and  Use. 
Second  Edition,  corrected.  265  Illustrations.  8vo.,  cloth,  501  pp. 

Net,  $4.00 

WALKER,  FREDERICK.  Practical  Dynamo-Building  for  Amateurs. 
How  to  Wind  for  any  Output.  Third  Edition.  Illustrated.  16mo., 
cloth,  104  pp.  (No.  98  Van  Nostrand's  Science  Series.) 50  cents 

—  SYDNEY  F.  Electricity  in  Homes  and  Workshops.  A  Practical 
Treatise  on  Auxiliary  Electrical  Apparatus.  Fourth  Edition.  Illus- 
trated. 12mo.,  cloth,  358  pp $2 .00 

Electricity  in  Mining.     Illustrated.     8vo.,  cloth,  385  pp $3.50 

Electric  Wiring  and  Fitting  for  Plumbers  and  Gasfitters.  94  Illustrations. 
12mo.,  cloth,  160  pp Net,  $2 . 50 

WALLING,  B.  T.,  Lieut.-Com.  U.S.N.,  and  MARTIN,  JULIUS.  Electtical 
Installations  of  the  United  States  Navy.  With  many  Diagrams  arid 
Engravings.  8vo.,  cloth,  648  pp $6 .00 

WALMSLEY,  R.  M.  Electricity  in  the  Service  of  Man.  A  Popular  and 
Practical  Treatise  on  the  Application  of  Electricity  in  Modern  Life. 
Illustrated.  8vo.,  cloth,  1208  pp Net,  $4 . 50 

WATSON,  A.  E.  Storage  Batteries,  their  Theory,  Construction  and  Use. 
Illustrated.  12mo.,  cloth,  100  pp $1 .50 


WATT,  ALEXANDER.  Electroplating  and  Refining  of  Metals.  New 
Edition,  rewritten  by  Arnold  Philip.  Illustrated.  8vo.,  cloth,  677 

PP Net,  $4.50 

Electrometallurgy.     Fifteenth  Edition.      Illustrated.      12mo.,  cloth,  225 
PP $1.00 

WEBB,  H.  L.  A  Practical  Guide  to  the  Testing  of  Insulated  Wires  and 
Cables.  Fifth  Edition.  Illustrated.  12mo.,  cloth,  118  pp $1.00 

WEEKS,  R.  W.      The  Design  of  Alternate-Current  Transformer. 

New  Edition  in  Press 

WEYMOUTH,  F.  MARTEN.  Drum  Armatures  and  Commutators. 
(Theory  and  Practice.)  A  complete  treatise  on  the  theory  and  con- 
struction of  drum-winding,  and  of  commutators  for  closed-coil  arma- 
tures, together  with  a  full  resum6  of  some  of  the  principal  points 
involved  in  their  design,  and  an  exposition  of  armature  reactions 
and  sparking.  Illustrated.  8vo.,  cloth,  295  pp Net,  $3.00 

WILKINSON,  H.  D.  Submarine  Cable  Laying  and  Repairing.  Second 
Edition,  completely  revised.  313  Illustrations.  8vo.,  cloth,  580  pp. 

Net,  $6 . 00 

YOUNG,  J.  ELTON.  Electrical  Testing  for  Telegraph  Engineers.  Illus- 
trated. 8vo.,  cloth,  264  pp Net,  $4.00 

ZEIDLER,  J.,  and  LUSTGARTEN,  J.  Electric  Arc  Lamps:  Their  Princi- 
ples, Construction  and  Working.  160  Illustrations.  8vo.,  cloth, 
188  pp Net,  $2.00 


A  p6=page  Catalog  of  Books  on  Electricity,  classified  by 
subjects,  will  be  furnished  gratis,  postage  prepaid, 
on  application. 


OCT  25   193 


I 


203792 


